Neuromorphic computing aims at mimicking the synapses, dendrites, and neurons in the brain as well as their associated connected networks to perform a variety of complex tasks including sensing, computing, perception, sometimes by directly utilizing the physical properties of materials. Their functionality diversity and performance highly depend on the use of materials. Compared to the conventional materials, 2D materials exhibit many unique physical properties and the research of 2D materials has reshaped the field of neuromorphic computing. This special issue presents some of the innovations in using devices based on 2D materials to emulate the biological synapses or generate noise injection to hardware neural networks. The issue also provides a comprehensive analysis of recent advances in exploiting the unique physical properties of 2D materials for neuromorphic computing. These innovations and analysis may serve as a useful guide to further advance 2D materials for practical applications. This special issue includes two research articles and four review articles, with contents briefly summarized in the following paragraphs.