The demand for advanced neuromorphic systems has surged due to their potential in artificial intelligence, robotics, and brain-computer interfaces. Artificial synapses are core elements in implementing hardware neuromorphic systems. Within the diverse realm of synaptic devices, electrochemical iontronic synapses (EISs) have gained prominence in recent years. EIS devices closely replicate natural synaptic mechanisms by precisely regulating ion concentrations within active regions, reversibly modulating conductivity based on the local perturbation of the electronic structure. EISs, guided by biomimetic electrochemistry, provide unique advantages such as precise weight modulation, consistent performance, low energy consumption, and rapid switching. Their adaptability to various ions and materials solidifies their applicability as neural network accelerators. In this review, we comprehensively explore EIS devices, examining their fundamental principles, recent progress, and forthcoming challenges. EISs hold the potential to bridge the gap between artificial and biological neural networks, offering a pathway to advanced hardware networks.