Stretchable　synaptic　transistors,　a　core　technology　in　neuromorphic　electronics,　have　functions　and　structures　similar　to　biological　synapses　and　can　concurrently　transmit　signals　and　learn.　Stretchable　synaptic　transistors　are　usually　soft　and　stretchy　and　can　accommodate　various　mechanical　deformations,　which　presents　significant　prospects　in　soft　machines,　electronic　skin,　human-brain　interfaces,　and　wearable　electronics.　Considerable　efforts　have　been　devoted　to　developing　stretchable　synaptic　transistors　to　implement　electronic　device　neuromorphic　functions,　and　remarkable　advances　have　been　achieved.　Here,　this　review　introduces　the　basic　concept　of　artificial　synaptic　transistors　and　summarizes　the　recent　progress　in　device　structures,　functional-layer　materials,　and　fabrication　processes.　Classical　stretchable　synaptic　transistors,　including　electric　double-layer　synaptic　transistors,　electrochemical　synaptic　transistors,　and　optoelectronic　synaptic　transistors,　as　well　as　the　applications　of　stretchable　synaptic　transistors　in　light-sensory　systems,　tactile-sensory　systems,　and　multisensory　artificial-nerves　systems,　are　discussed.　Finally,　the　current　challenges　and　potential　directions　of　stretchable　synaptic　transistors　are　analyzed.　This　review　presents　a　detailed　introduction　to　the　recent　progress　in　stretchable　synaptic　transistors　from　basic　concept　to　applications,　providing　a　reference　for　the　development　of　stretchable　synaptic　transistors　in　the　future.