: The emergence of Memristor offers new avenues to look at several potential applications ranging from non-volatile memories to neuromorphic system. A typical sign of the physical memristor device is Pinched Hysteresis Loop. In order to mimic this loop with high accuracy, several memristor models have been evolved in the past. Moreover, various mathematical window functions have been developed from the researchers to throw more insight into the memristor model with the accordance of enhancing the degree of nonlinearity, resolving boundary effect and boundary lock. This review portrays a brief description of explored memristor models and window functions. With this, a comprehensive analysis is made to depict the advantages and disadvantages in a more explicit manner. Furthermore, this work exhibits the prevailing properties of memristor along with the different types of switching mechanisms. Here, the future perspective of the memristive technology is also explored very well as the memristor became an innovative candidate in the memory technology over the semiconductor. And a brief discussion of memristor based potential applications, such as a fine resolution programmable gain amplifier, synapse, and logic gate are explained as well.