Functional emulation of biological synapses using electronic devices is regarded as the first step toward neuromorphic engineering and artificial neural networks (ANNs). Electrolyte-gated transistors (EGTs) are mixed ionic-electronic conductivity devices capable of efficient gate-channel capacitance coupling, biocompatibility, and flexible architectures. Electrolyte gating offers significant advantages for the realization of neuromorphic devices/architectures, including ultralow-voltage operation and the ability to form parallel-interconnected networks with minimal hardwired connectivity. In this review, the most recent developments in EGT-based electronics are introduced with their synaptic behaviors and detailed mechanisms, including short-/long-term plasticity, global regulation phenomena, lateral coupling between device terminals, and spatiotemporal correlated functions. Analog memory phenomena allow for the implementation of perceptron-based ANNs. Due to their mixed-conductivity phenomena, neuromorphic circuits based on EGTs allow for facile interfacing with biological environments. We also discuss the future challenges in implementing low power, high speed, and reliable neuromorphic computing for large-scale ANNs with these neuromorphic devices. The advancement of neuromorphic devices that rely on EGTs highlights the importance of this field for neuromorphic computing and for novel healthcare technologies in the form of adaptable or trainable biointerfacing.