The incorporation of 2D materials into memristive devices has boosted advancements in non-volatile memory (NVM), and other related applications including brain inspired neuromorphic systems, artificial intelligence (AI)-machine learning (ML), optoelectronics, photonics, implementing arithmetic operations, and hybrid CMOS architectures. These advancements have taken place among limitations on silicon-based flash and surging data demands, stimulating the research of innovative materials and architectures, particularly for the next generation memory devices. This comprehensive review expands upon the cutting-edge developments in 2D material-based memristors, including their fabrication techniques, performance evaluation, fundamental properties, diverse applications, further challenges in their modernization, and future road map. By emphasizing the distinct characteristics of 2D materials, we reviewed their memristive behavior and highlighted the major contributions by leading researchers over the years. Focus of this review is on the incorporation of graphene (derivatives of graphene), transition metal dichalcogenides (TMDs), and other 2D materials (like MXenes and nanocomposites) in various memristive architectures. The review paper systematically explored the specific roles of graphene and other 2D materials in memristor devices including their use as electrodes, active layers, barrier layers, interfacial layers, and tunnel layers. The major challenges faced by the 2D material based memristor technology hindering their advancement have been critically reviewed including the scalability, yield, hardware implementation, performance enhancement, fabrication techniques, material/device engineering, and commercialization of these devices. Workable solutions to those problems along with the clear and comprehensive road map of future directions for addressing these hurdles have been recommended to unlock the full potential of this transitional technology. This review provides an authoritative resource and compelling rationale for researchers working towards metamorphic memristor solutions by emphasizing the imperative role of 2D materials.