Constructor and destructor are special types of methods in object-oriented programming. Constructors are used to initialize objects and are called when an object is created, while destructors are used to destroy objects and are called when an object is deleted or goes out of scope. There are different types of constructors like default, parameterized, and copy constructors. Constructors cannot be inherited or virtual. Destructors are used to clean up resources used by an object and are called automatically when an object is destroyed. The key differences between constructors and destructors are that constructors initialize objects and can have parameters, while destructors destroy objects and have no parameters.