Hydrogel-gated synaptic transistors offer unique advantages, including biocompatibility, tunable electrical properties, being biodegradable, and having an ability to mimic biological synaptic plasticity. For processing massive data with ultralow power consumption due to high parallelism and human brain-like processing abilities, synaptic transistors have been widely considered for replacing von Neumann architecture-based traditional computers due to the parting of memory and control units. The crucial components mimic the complex biological signal, synaptic, and sensing systems. Hydrogel, as a gate dielectric, is the key factor for ionotropic devices owing to the excellent stability, ultra-high linearity, and extremely low operating voltage of the biodegradable and biocompatible polymers. Moreover, hydrogel exhibits ionotronic functions through a hybrid circuit of mobile ions and mobile electrons that can easily interface between machines and humans. To determine the high-efficiency neuromorphic chips, the development of synaptic devices based on organic field effect transistors (OFETs) with ultra-low power dissipation and very large-scale integration, including bio-friendly devices, is needed. This review highlights the latest advancements in neuromorphic computing by exploring synaptic transistor developments. Here, we focus on hydrogel-based ionic-gated three-terminal (3T) synaptic devices, their essential components, and their working principle, and summarize the essential neurodegenerative applications published recently. In addition, because hydrogel-gated FETs are the crucial members of neuromorphic devices in terms of cutting-edge synaptic progress and performances, the review will also summarize the biodegradable and biocompatible polymers with which such devices can be implemented. It is expected that neuromorphic devices might provide potential solutions for the future generation of interactive sensation, memory, and computation to facilitate the development of multimodal, large-scale, ultralow-power intelligent systems.