Neuromorphic computing systems, which mimic the operation of neurons and synapses in the human brain, are seen as an appealing next-generation computing method due to their strong and efficient computing abilities. Two-dimensional (2D) materials with dangling bond-free surfaces and atomic-level thicknesses have emerged as promising candidates for neuromorphic computing hardware. As a result, 2D neuromorphic devices may provide an ideal platform for developing multifunctional neuromorphic applications. Here, we review the recent neuromorphic devices based on 2D material and their multifunctional applications. The synthesis and next micro–nano fabrication methods of 2D materials and their heterostructures are first introduced. The recent advances of neuromorphic 2D devices are discussed in detail using different operating principles. More importantly, we present a review of emerging multifunctional neuromorphic applications, including neuromorphic visual, auditory, tactile, and nociceptive systems based on 2D devices. In the end, we discuss the problems and methods for 2D neuromorphic device developments in the future. This paper will give insights into designing 2D neuromorphic devices and applying them to the future neuromorphic systems.