In this paper, a brief introduction to memristor device will be presented. Since 1971, memristor device invented by Leo Chua which included in the fundamental electrical elements besides resistors, capacitors and inductors. Memristor consider as the missing elements that correlate between the flux and the charges of the electrons. Memristor was not realized as a physical component until recently. HP and Knowm are the available physical memristor device in the market with different structure. However, HP memristor is considered to be the most structure have been studied from the researchers. Now a days considered is the core element in AI accelerators which depends on memory processor structure. This paper will discuss the history of memristor and its structure based on HP and Knowm approach with mathematical models. Some fabrication techniques will be discussed and the applications.This paper will discuss the history of memristor and its structure based on HP and Knowm approach with mathematical models. Some fabrication techniques will be discussed and the applications.