Memristor is an electrical component which regulates the flow of electrical current in a circuit and can remember the amount of charge that has previously flowed through it. Memristors are non-volatile and are important to resist the current variations. They change resistance according to the current variations flowing in them. Memristor is the fourth fundamental circuit element joining the resistor, capacitor and inductor. It maintains relation between time integrals of current and voltage across two terminal elements. It has the potential to enhance several areas of integrated circuit designs and computing. The first memristor was manufactured at HP laboratories. Memristors can be made to perform in an analog manner. In order to provide digital memory, these can be used at their extreme values. The global Memristor market can be segmented based on applications into Nano Electronic Memories, Computer Logic, Neuromorphic Computer Architecture, Replacement of Transistors, Programmable ...