For nearly 180 years, circuit theory is studied with three fundamental circuit elements, the resistor, the capacitor and the inductor. These passive two terminal elements describe the relations between voltage, current, charge and flux but do not store information. On this back ground, in 1971 Prof. Leon .O. Chua presented a revolutionary concept of the existence of the fourth missing element called “Memristor” in the list of three basic electrical circuit elements. Introduction of the nano scale Memristor (Resistor with Memory) that can store information without the need of a power source is a paradigm change in fundamental circuit elements [1, 2, 3]. Memristor has tremendous potential to replace conventional flash memories in near future. Its emerging applications include a wide range from analog /digital computation circuits to neuromorphic circuits. Introduction of non linear Memristor is enhancing the quantum computing processing and understanding of biological processes [4]. Due to its novel characteristics and diversifying application potentials, nano scale Memristor is getting a lime light focus from researchers as well as from industry. This paper will discuss the fundamental properties, basic device model and prominent application areas of Memristor as an advancement in fundamental circuit element.