Current computing systems rely on Boolean logic and von Neumann architecture, where computing cells are based on high-speed electron-conducting complementary metal-oxide-semiconductor (CMOS) transistors. In contrast, ions play an essential role in biological neural computing. Compared with CMOS units, the synapse/neuron computing speed is much lower, but the human brain performs much better in many tasks such as pattern recognition and decision-making. Recently, ionic dynamics in oxide electrolyte-gated transistors have attracted increasing attention in the field of neuromorphic computing, which is more similar to the computing modality in the biological brain. In this review article, we start with the introduction of some ionic processes in biological brain computing. Then, electrolyte-gated ionic transistors, especially oxide ionic transistors, are briefly introduced. Later, we review the state-of-the-art progress in oxide electrolyte-gated transistors for ionic neuromorphic computing including dynamic synaptic plasticity emulation, spatiotemporal information processing, and artificial sensory neuron function implementation. Finally, we will address the current challenges and offer recommendations along with potential research directions.