Recently, two-dimensional (2D) materials and their heterostructures have been recognized as the foundation for future brain-like neuromorphic computing devices. Two-dimensional materials possess unique characteristics such as near-atomic thickness, dangling-bond-free surfaces, and excellent mechanical properties. These features, which traditional electronic materials cannot achieve, hold great promise for high-performance neuromorphic computing devices with the advantages of high energy efficiency and integration density. This article provides a comprehensive overview of various 2D materials, including graphene, transition metal dichalcogenides (TMDs), hexagonal boron nitride (h-BN), and black phosphorus (BP), for neuromorphic computing applications. The potential of these materials in neuromorphic computing is discussed from the perspectives of material properties, growth methods, and device operation principles.