Polymorphism and inheritance are key concepts in object-oriented programming. Polymorphism allows objects to take on multiple forms, and there are two types: compile-time polymorphism achieved through function/operator overloading, and runtime polymorphism achieved through method overriding. Inheritance allows a class to inherit properties and behaviors from a parent class, and there are two types of inheritance: single inheritance where a class inherits from one parent class, and multi-level inheritance where a class can inherit from a parent class that itself inherits from another parent class.