The scalability of two-dimensional (2D) materials down to a single monolayer offers exciting prospects for high-speed, energy-efficient, scalable memristors. This review highlights the development of 2D material-based memristors and potential applications beyond memory, including neuromorphic, in-memory, in-sensor, and complex computing. This review also encompasses potential challenges and future opportunities for advancing these materials and technologies, underscoring the transformative impact of 2D memristors on versatile and sustainable electronic devices and systems.