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 the aspect of accomplishing 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 and the different types of switching mechanisms. Here, the future perspective of the memristive technology is also explored very well as the memristor has become an innovative candidate in the memory technology over the semiconductor. Memristor-based potential applications such as a fine resolution programmable gain amplifier, synapse, and logic gate are also explained briefly. © 2020 Bentham Science Publishers.