With the advent of Big Data, traditional digital computing is struggling to cope with intricate tasks related to data classification or pattern recognition. To mitigate this limitation, software‐based neural networks are implemented, but they are run in conventional computers whose operation principle (with separate memory and data‐processing units) is highly inefficient compared to the human brain. Brain‐inspired in‐memory computing is achieved through a wide variety of methods, for example, artificial synapses, spiking neural networks, or reservoir computing. However, most of these methods use materials (e.g., memristor arrays, spintronics, phase change memories) operated with electric currents, resulting in significant Joule heating effect. Tuning magnetic properties by voltage‐driven ion motion (i.e., magnetoionics) has recently emerged as an alternative energy‐efficient approach to emulate functionalities of biological synapses: potentiation/depression, multilevel storage, or transitions from short‐term to long‐term plasticity. In this perspective, the use of magnetoionics in neuromorphic applications is critically reviewed, with emphasis on modulating synaptic weight through: 1) control of magnetization by voltage‐induced ion retrieval/insertion; and 2) control of magnetic stripe domains and skyrmions in gated magnetic thin films adjacent to solid‐state ionic supercapacitors. The potential prospects in this emerging research area together with a forward‐looking discussion on future opportunities are provided.