Objects in JavaScript can be created using object literals, the new keyword, or Object.create(). Objects are collections of properties and methods that are mutable and manipulated by reference. Arrays are objects that represent ordered collections of values of any type and are created using array literals or the Array constructor. Common array methods include concat, join, pop, push, reverse, and sort. The Math object provides common mathematical functions like pow, round, ceil, floor, random, and trigonometric functions.