Two-dimensional (2D) layered materials have recently gained significant attention and have been extensively studied for their potential applications in neuromorphic computing, where they are used to mimic the functions of the human brain. Their unique properties, including atomic-level thickness, exceptional mechanical stability, and tunable optical and electrical characteristics, make them highly versatile for a wide range of applications. In this review, we offer a comprehensive analysis of 2D material-based memristors. Furthermore, we examine the ability of 2D material-based memristors to successfully mimic the human brain by referencing their neuromorphic applications.