diff --git a/src/document.ts b/src/document.ts
index 7130a06..26d8355 100644
--- a/src/document.ts
+++ b/src/document.ts
@@ -7,7 +7,7 @@ const cloneDeep = rfdc();
 
 abstract class Document<T> {
   abstract _model: Model<T>;
-  _id!: string | number | undefined;
+  _id!: string;
   abstract _schema: Schema<T>;
   [key : string]: any;
 
diff --git a/src/model.ts b/src/model.ts
index 3db7b58..ba924b2 100644
--- a/src/model.ts
+++ b/src/model.ts
@@ -11,7 +11,7 @@ import WarehouseError from './error';
 import PopulationError from './error/population';
 import Mutex from './mutex';
 import type Database from './database';
-import type { AddSchemaTypeOptions, NodeJSLikeCallback, Options } from './types';
+import type { AddSchemaTypeOptions, NodeJSLikeCallback, Options, queryCallback } from './types';
 
 class Model<T> extends EventEmitter {
   _mutex = new Mutex();
@@ -236,7 +236,7 @@ class Model<T> extends EventEmitter {
    * @return {BluebirdPromise}
    * @private
    */
-  _updateWithStack(id: string | number, stack: ((data: T) => void)[]): BluebirdPromise<any> {
+  _updateWithStack(id: string, stack: queryCallback<T>[]): BluebirdPromise<any> {
     const schema = this.schema;
 
     const data = this.data[id];
@@ -278,7 +278,7 @@ class Model<T> extends EventEmitter {
    * @param {function} [callback]
    * @return {BluebirdPromise}
    */
-  updateById(id: string | number, update: object, callback?: NodeJSLikeCallback<any>): BluebirdPromise<any> {
+  updateById(id: string, update: object, callback?: NodeJSLikeCallback<any>): BluebirdPromise<any> {
     return BluebirdPromise.using(this._acquireWriteLock(), () => {
       const stack = this.schema._parseUpdate(update);
       return this._updateWithStack(id, stack);
@@ -305,7 +305,7 @@ class Model<T> extends EventEmitter {
    * @return {BluebirdPromise}
    * @private
    */
-  _replaceById(id: string | number, data_: Document<T> | T): BluebirdPromise<any> {
+  _replaceById(id: string, data_: Document<T> | T): BluebirdPromise<any> {
     const schema = this.schema;
 
     if (!this.has(id)) {
@@ -339,7 +339,7 @@ class Model<T> extends EventEmitter {
    * @param {function} [callback]
    * @return {BluebirdPromise}
    */
-  replaceById(id: string | number, data: Document<T> | T, callback?: NodeJSLikeCallback<any>): BluebirdPromise<any> {
+  replaceById(id: string, data: Document<T> | T, callback?: NodeJSLikeCallback<any>): BluebirdPromise<any> {
     return BluebirdPromise.using(this._acquireWriteLock(), () => this._replaceById(id, data)).asCallback(callback);
   }
 
@@ -362,7 +362,7 @@ class Model<T> extends EventEmitter {
    * @return {BluebirdPromise}
    * @private
    */
-  _removeById(id: string | number): BluebirdPromise<any> {
+  _removeById(id: string): BluebirdPromise<any> {
     const schema = this.schema;
 
     const data = this.data[id];
@@ -389,7 +389,7 @@ class Model<T> extends EventEmitter {
    * @param {function} [callback]
    * @return {BluebirdPromise}
    */
-  removeById(id: string | number, callback?: NodeJSLikeCallback<any>): BluebirdPromise<any> {
+  removeById(id: string, callback?: NodeJSLikeCallback<any>): BluebirdPromise<any> {
     return BluebirdPromise.using(this._acquireWriteLock(), () => this._removeById(id)).asCallback(callback);
   }
 
@@ -531,7 +531,10 @@ class Model<T> extends EventEmitter {
    * @param {String|Number} [order]
    * @return {Query}
    */
-  sort(orderby: string | object, order?: string | number | object): Query<T> {
+  sort(orderby: string, order: 'desc' | number | Record<string, any>): Query<T>;
+  sort(orderby: string): Query<T>;
+  sort(orderby: Record<string, number | Record<string, any>>): Query<T>;
+  sort(orderby: string | Record<string, number | Record<string, any>>, order?: 'desc' | number | Record<string, any>): Query<T> {
     const sort = parseArgs(orderby, order);
     const fn = this.schema._execSort(sort);
 
diff --git a/src/query.ts b/src/query.ts
index dae0f58..fcb8906 100644
--- a/src/query.ts
+++ b/src/query.ts
@@ -201,14 +201,17 @@ abstract class Query<T> {
    * query.sort('-date title');
    * ```
    *
-   * If the `order` equals to `-1`, `desc` or `descending`, the data will be
+   * If the `order` equals to `-1` or `desc`, the data will be
    * returned in reversed order.
    *
    * @param {String|Object} orderby
    * @param {String|Number} [order]
    * @return {Query}
    */
-  sort(orderby: string | object, order?: string | number | object): Query<T> {
+  sort(orderby: string, order: 'desc' | number | Record<string, any>): Query<T>;
+  sort(orderby: string): Query<T>;
+  sort(orderby: Record<string, number | Record<string, any>>): Query<T>;
+  sort(orderby: string | Record<string, number | Record<string, any>>, order?: 'desc' | number | Record<string, any>): Query<T> {
     const sort = parseArgs(orderby, order);
     const fn = this._schema._execSort(sort);
 
diff --git a/src/schema.ts b/src/schema.ts
index d6229d6..7ceb42a 100644
--- a/src/schema.ts
+++ b/src/schema.ts
@@ -5,45 +5,24 @@ import { getProp, setProp, delProp } from './util';
 import PopulationError from './error/population';
 import SchemaTypeVirtual from './types/virtual';
 import { isPlainObject } from 'is-plain-object';
-import type { AddSchemaTypeLoopOptions, AddSchemaTypeOptions, Options, SchemaTypeOptions } from './types';
+import type { AddSchemaTypeLoopOptions, AddSchemaTypeOptions, AddSchemaTypeSimpleOptions, Options, queryCallback, queryFilterCallback, queryParseCallback, SchemaTypeOptions } from './types';
 import type Model from './model';
-
-/**
- * @callback queryFilterCallback
- * @param {*} data
- * @return {boolean}
- */
-type queryFilterCallback = (data: unknown) => boolean;
-
-/**
- * @callback queryCallback
- * @param {*} data
- * @return {void}
- */
-type queryCallback = (data: unknown) => void;
-
-/**
- * @callback queryParseCallback
- * @param {*} a
- * @param {*} b
- * @returns {*}
- */
-type queryParseCallback = (a: unknown, b: unknown) => number;
+import type Document from './document';
 
 const builtinTypes = new Set(['String', 'Number', 'Boolean', 'Array', 'Object', 'Date', 'Buffer']);
 
-const getSchemaType = (name: string, options: { type: SchemaTypeOptions; [key: string]: any } | SchemaTypeOptions) => {
-  const Type = (options as any).type || options;
-  const typeName: string = Type.name;
+const getSchemaType = (name: string, options: AddSchemaTypeSimpleOptions): SchemaType<any> => {
+  const Type: SchemaTypeOptions = (options as any).type || options;
+  const typeName = Type.name;
 
   if (builtinTypes.has(typeName)) {
     return new Types[typeName](name, options);
   }
 
-  return new Type(name, options);
+  return new Type(name, options as Exclude<AddSchemaTypeSimpleOptions, SchemaTypeOptions>);
 };
 
-const checkHookType = (type: string) => {
+const checkHookType = (type: string): void => {
   if (type !== 'save' && type !== 'remove') {
     throw new TypeError('Hook type must be `save` or `remove`!');
   }
@@ -57,13 +36,10 @@ const hookWrapper = (fn: (...args: any[]) => void): (...args: any[]) => Bluebird
   return BluebirdPromise.method(fn);
 };
 
-/**
- * @param {Function[]} stack
- */
-const execSortStack = (stack: ((a: unknown, b: unknown) => number)[]) => {
+const execSortStack = <T = any>(stack: queryParseCallback<Document<T>>[]): queryParseCallback<Document<T>> => {
   const len = stack.length;
 
-  return (a: any, b: any) => {
+  return (a: Document<T>, b: Document<T>) => {
     let result: number;
 
     for (let i = 0; i < len; i++) {
@@ -75,11 +51,11 @@ const execSortStack = (stack: ((a: unknown, b: unknown) => number)[]) => {
   };
 };
 
-const sortStack = (path_: SchemaType<any>, key: string, sort: string | number) => {
+const sortStack = <T = any>(path_: SchemaType<any>, key: string, sort: string | number): queryParseCallback<Document<T>> => {
   const path = path_ || new SchemaType(key);
   const descending = sort === 'desc' || sort === -1;
 
-  return (a: any, b: any) => {
+  return (a: Document<T>, b: Document<T>) => {
     const result = path.compare(getProp(a, key), getProp(b, key));
     return descending && result ? result * -1 : result;
   };
@@ -90,7 +66,7 @@ class UpdateParser {
     return (data: any) => { setProp(data, key, update); };
   }
 
-  static updateStackOperator(path_: SchemaType<unknown>, ukey: string | number, key: string, update: any) {
+  static updateStackOperator(path_: SchemaType<unknown>, ukey: string, key: string, update: any) {
     const path = path_ || new SchemaType(key);
 
     return (data: any) => {
@@ -109,7 +85,7 @@ class UpdateParser {
    * @param {queryCallback[]} [stack]
    * @private
    */
-  parseUpdate(updates: object, prefix = '', stack: queryCallback[] = []): queryCallback[] {
+  parseUpdate<T>(updates: object, prefix = '', stack: queryCallback<T>[] = []): queryCallback<T>[] {
     const { paths } = this;
     const { updateStackOperator } = UpdateParser;
     const keys = Object.keys(updates);
@@ -181,7 +157,7 @@ class QueryParser {
   queryStackOperator(qkey: string, name: string, query: any): queryFilterCallback {
     const path = this.paths[name] || new SchemaType(name);
 
-    return data => path[qkey](getProp(data, name), query, data);
+    return (data: unknown) => path[qkey](getProp(data, name), query, data);
   }
 
   /**
@@ -190,7 +166,7 @@ class QueryParser {
    * @return {void}
    * @private
    */
-  $and(arr: any[], stack: queryFilterCallback[]): void {
+  $and(arr: object[], stack: queryFilterCallback[]): void {
     for (let i = 0, len = arr.length; i < len; i++) {
       stack.push(this.execQuery(arr[i]));
     }
@@ -201,7 +177,7 @@ class QueryParser {
    * @return {queryFilterCallback}
    * @private
    */
-  $or(query: any[]): queryFilterCallback {
+  $or(query: object[]): queryFilterCallback {
     const stack = this.parseQueryArray(query);
     const len = stack.length;
 
@@ -219,7 +195,7 @@ class QueryParser {
    * @return {queryFilterCallback}
    * @private
    */
-  $nor(query: any[]): queryFilterCallback {
+  $nor(query: object[]): queryFilterCallback {
     const stack = this.parseQueryArray(query);
     const len = stack.length;
 
@@ -237,7 +213,7 @@ class QueryParser {
    * @return {queryFilterCallback}
    * @private
    */
-  $not(query: any): queryFilterCallback {
+  $not(query: object): queryFilterCallback {
     const stack = this.parseQuery(query);
     const len = stack.length;
 
@@ -261,7 +237,7 @@ class QueryParser {
    * @return {queryFilterCallback}
    * @private
    */
-  $where(fn: (...args: any[]) => boolean): queryFilterCallback {
+  $where(fn: () => boolean): queryFilterCallback {
     return data => Reflect.apply(fn, data, []);
   }
 
@@ -272,8 +248,8 @@ class QueryParser {
    * @return {queryFilterCallback[]}
    * @private
    */
-  parseQueryArray(arr: any[]): queryFilterCallback[] {
-    const stack = [];
+  parseQueryArray(arr: object[]): queryFilterCallback[] {
+    const stack: queryFilterCallback[] = [];
     this.$and(arr, stack);
     return stack;
   }
@@ -315,7 +291,7 @@ class QueryParser {
    * @return {queryFilterCallback[]}
    * @private
    */
-  parseQuery(queries: any): queryFilterCallback[] {
+  parseQuery(queries: object): queryFilterCallback[] {
 
     /** @type {queryFilterCallback[]} */
     const stack: queryFilterCallback[] = [];
@@ -573,7 +549,7 @@ class Schema<T = any> {
    * @param {String} type Hook type. One of `save` or `remove`.
    * @param {Function} fn
    */
-  pre(type: 'save' | 'remove', fn: (...args: any[]) => void): void {
+  pre(type: keyof Schema['hooks']['pre'], fn: (...args: any[]) => void): void {
     checkHookType(type);
     if (typeof fn !== 'function') throw new TypeError('Hook must be a function!');
 
@@ -586,7 +562,7 @@ class Schema<T = any> {
    * @param {String} type Hook type. One of `save` or `remove`.
    * @param {Function} fn
    */
-  post(type: 'save' | 'remove', fn: (...args: any[]) => void): void {
+  post(type: keyof Schema['hooks']['post'], fn: (...args: any[]) => void): void {
     checkHookType(type);
     if (typeof fn !== 'function') throw new TypeError('Hook must be a function!');
 
@@ -696,7 +672,7 @@ class Schema<T = any> {
    * @return {queryCallback[]}
    * @private
    */
-  _parseUpdate(updates: object): queryCallback[] {
+  _parseUpdate(updates: object): queryCallback<T>[] {
     return new UpdateParser(this.paths).parseUpdate(updates);
   }
 
@@ -721,7 +697,7 @@ class Schema<T = any> {
    * @return {queryParseCallback[]}
    * @private
    */
-  _parseSort(sorts: object, prefix = '', stack: queryParseCallback[] = []): queryParseCallback[] {
+  _parseSort(sorts: Record<string, number | string | Record<string, any>>, prefix = '', stack: queryParseCallback<Document<T>>[] = []): queryParseCallback<Document<T>>[] {
     const { paths } = this;
     const keys = Object.keys(sorts);
 
@@ -747,7 +723,7 @@ class Schema<T = any> {
    * @return {queryParseCallback}
    * @private
    */
-  _execSort(sorts: object): queryParseCallback {
+  _execSort(sorts: Record<string, number | string | Record<string, any>>): queryParseCallback<Document<T>> {
     const stack = this._parseSort(sorts);
     return execSortStack(stack);
   }
diff --git a/src/types.ts b/src/types.ts
index 16d85d9..31a4589 100644
--- a/src/types.ts
+++ b/src/types.ts
@@ -1,6 +1,10 @@
 import type SchemaType from './schematype';
 
-export type NodeJSLikeCallback<R, E = any> = (err: E, result?: R) => void
+interface Constructor {
+  new (...args: any[]): any;
+}
+
+export type NodeJSLikeCallback<R, E = any> = (err: E, result?: R) => void;
 
 export interface Options {
   lean: boolean;
@@ -12,14 +16,33 @@ export interface Options {
   model: string;
 }
 
-export type SchemaTypeOptions = typeof SchemaType<unknown> | SchemaType<unknown> | ((...args: any[]) => any)
+export type SchemaTypeOptions = typeof SchemaType<unknown> | Constructor;
 
-export type AddSchemaTypeSimpleOptions = SchemaTypeOptions | { type: SchemaTypeOptions; [key: string]: any };
+export type AddSchemaTypeSimpleOptions =
+  | SchemaTypeOptions
+  | {
+      type: SchemaTypeOptions;
+      required?: boolean;
+      default?: (() => any) | any;
+      [key: string]: any;
+    };
 
-export type AddSchemaTypeMixedOptions = AddSchemaTypeSimpleOptions | AddSchemaTypeSimpleOptions[];
+export type AddSchemaTypeMixedOptions =
+  | AddSchemaTypeSimpleOptions
+  | []
+  | [AddSchemaTypeSimpleOptions];
 
 export interface AddSchemaTypeLoopOptions {
   [key: string]: AddSchemaTypeMixedOptions | AddSchemaTypeLoopOptions;
 }
 
-export type AddSchemaTypeOptions = AddSchemaTypeMixedOptions | AddSchemaTypeLoopOptions;
+export type AddSchemaTypeOptions =
+  | AddSchemaTypeMixedOptions
+  | AddSchemaTypeLoopOptions
+  | SchemaType<unknown>;
+
+export type queryFilterCallback = (data: unknown) => boolean;
+
+export type queryCallback<T> = (data: T) => void;
+
+export type queryParseCallback<T> = (a: T, b: T) => number;
diff --git a/src/util.ts b/src/util.ts
index aabb518..301279d 100644
--- a/src/util.ts
+++ b/src/util.ts
@@ -6,7 +6,7 @@ function _parseArgs(args: string): Record<string, number> {
   if (typeof args !== 'string') return args;
 
   const arr = args.split(' ');
-  const result = {};
+  const result: Record<string, number> = {};
 
   for (let i = 0, len = arr.length; i < len; i++) {
     const key = arr[i];
@@ -173,8 +173,12 @@ export function reverse<T>(arr: T[]): T[] {
   return arr;
 }
 
-export function parseArgs(orderby: string | object, order?: string | number | object): Record<string, number> {
-  let result;
+export function parseArgs<B extends string, O extends number | string | Record<string, any>>(orderby: B, order: O): { [key in typeof orderby]: typeof order };
+export function parseArgs<B extends string, O>(orderby: B): Record<string, number>;
+export function parseArgs<B extends Record<string, number>, O>(orderby: B): B;
+export function parseArgs<B extends string | Record<string, number | Record<string, any>>, O extends number | string | Record<string, any>>(orderby: B, order?: O): Record<string, number | string | object>;
+export function parseArgs<B extends string | Record<string, number | Record<string, any>>, O extends number | string | Record<string, any>>(orderby: B, order?: O) {
+  let result: Record<string, number | string | Record<string, any>>;
 
   if (order) {
     result = {};