Artificial synapses emulate biological synaptic signals in neuromorphic systems to attain brain-like computation and autonomous learning behaviors in non-von-Neumann systems. Several classes of materials have been applied to this field to achieve numerous functionalities of biological synapses. Nanomaterials (NMs), such as one-dimensional (1D) and two-dimensional (2D) NMs have shown great potential due to their nanometer feature size (1D) and molecular-level thickness (2D). In this paper, we review the development of artificial synapses, and discuss state-of-the-art artificial synapses based on NMs.