Currently, neuromorphic computing is regarded as the most efficient way to solve the von Neumann bottleneck. Transistor-based devices have been considered suitable for emulating synaptic functions in neuromorphic computing due to their synergistic control capabilities on synaptic weight changes. Various low-dimensional inorganic materials such as silicon nanomembranes, carbon nanotubes, nanoscale metal oxides, and two-dimensional materials are employed to fabricate transistor-based synaptic devices. Although these transistor-based synaptic devices have progressed in terms of mimicking synaptic functions, their application in neuromorphic computing is still in its early stage. In this review, transistor-based synaptic devices are analyzed by categorizing them into different working mechanisms, and the device fabrication processes and synaptic properties are discussed. Future efforts that could be beneficial to the development of transistor-based synaptic devices in neuromorphic computing are proposed.