Abstract: Construction of brain-inspired systems that emulate the information processing capability of the human brain relies on studies of neuromorphic devices. Twodimensional materials, which possess excellent electric and photoelectric characteristics, multiple degrees of freedom of control, as well as great potential in three-dimensional vertical integration, provide the foundation of the device physics for designing multifunctional neuromorphic devices. In this article we present an overview of recent important progress associated with two-dimensional materials and van der Waals heterostructure neuromorphic devices, and also discuss future opportunities and challenges.