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Artificial synapses in neuromorphic computing systems hold potential to emulate biological synaptic plasticity to achieve brain-like computation and autonomous learning behaviors in non-von-Neumann systems. 2D materials, such as graphene, graphene oxide, hexagonal boron nitride, transition metal dichalcogenides, transition metal oxides, 2D perovskite, and black phosphorous, have been explored to achieve many functionalities of biological synapses due to their unique electronic, optoelectronic, electrochemical, and mechanical properties that are lacking in bulk materials. This review features the current development in the state-of-the-art artificial synaptic electronic devices based on 2D materials. The structures of these devices are first discussed according to their number of terminals (two-, three-, four-, and multi-terminals) and geometric layouts (vertical, horizontal, hybrid). Since different 2D materials have been utilized to fabricate these devices, their underlying physical mechanisms and principles are further discussed, and their artificial neuron synaptic functionalities and performances are analyzed and contrasted. Finally, a summary of the current research status and major achievements is concluded, and the outlooks and perspectives for this emerging and vibrant field and the potential applications of these devices for neuromorphic computing are presented. [ABSTRACT FROM AUTHOR]