Memristor is the contraction for memory and resistor, means memorable resistor, which can store information without the need of a power source. It was predicted in 1971 by Leon Chua as a “Missing Circuit Element” and was identified by R. Stanley Williams as a possible nanoscale device. In this paper, we review the concept and the mathematical definition of memristor, introduce the HP’s sandwich model of Pt／TiO2／Pt, and provide a fundamental analysis of the memristor behavior , such as pinched hysteretic loops. Finally, we discuss its application and research fields as a nanoscale device in the future.