To meet a growing demand for information processing, brain-inspired neuromorphic devices have been intensively studied in recent years. As an important type of neuromorphic device, synaptic devices have attracted strong attention. Among all the kinds of materials explored for the fabrication of synaptic devices, semiconductor nanocrystals (NCs) have become one of the preferred choices due to their excellent electronic and optical properties. In this review, we first introduce the research background of synaptic devices based on semiconductor NCs and briefly present the basic properties of semiconductor NCs. Recent developments in the field of synaptic devices based on semiconductor NCs are then discussed according to the materials employed in the active layers of the devices. Finally, we discuss existing problems and challenges of synaptic devices based on semiconductor NCs.