The progress of neural synaptic devices is experiencing an era of explosive growth. Given that the traditional storage system has yet to overcome the von Neumann bottleneck, it is critical to develop hardware with bioinspired information processing functions and lower power consumption. Transistors based on 2D materials, metal oxides, and organic materials have been adopted to mimic the synapse of a human brain, due to their high plasticity, parallel computing, integrated storage, and system information processing. Among these materials used to build transistors, organic semiconductors are considered to be the most promising candidate for neural synaptic devices and bio‐electronics, owing to their easy processing, mechanical flexibility, low cost, good bio‐compatibility, and ductility. This review focuses on the recent advances in organic synaptic devices with various structures, materials, and working mechanisms. The applications of artificial neural networks that integrate multiple organic synaptic transistors are also concretely discussed. Finally, the challenges that organic synaptic devices currently face are discussed and future developments are forecast. This review focuses on recent progress in organic synaptic devices. The organic materials used in synaptic devices, device structures, working mechanisms, and applications for organic‐based artificial neural systems are reviewed. The current problems and future perspectives regarding this emerging area are also discussed.