<p>Ion-conducting soft polymers, encompassing hydrogels, ionogels, and organic mixed ionic-electronic conductors, have emerged as distinctive material platforms for neuromorphic electronics, fundamentally diverging from the rigid paradigms of silicon and metal oxides. By enabling volumetric ionic transport and intricate electrochemical interactions within mechanically compliant matrices, these materials offer a biologically inspired route for emulating synaptic plasticity, memory consolidation, and adaptive sensing. With artificial synapses serving as the cornerstone of neuromorphic architectures, this review highlights recent advances in four classes of polymer-based composites: ion-gated transistors, electrochemical random-access memory cells, nanofluidic memristors, and soft ionic synapses. We dissect the physical mechanisms underlying plasticity: electric double-layer gating, volumetric electrochemical doping, nanofluidic confinement, and distinct viscoionic relaxation effects stemming from the macromolecular nature of the host matrix. Emphasis is placed on the interplay between ionic dynamics and polymer structural evolution in shaping the device functionality, energy efficiency, and multimodal responsiveness. We identify the critical challenges in switching speed, hydrolytic stability, and large-scale integration while highlighting emerging opportunities at the interface of biology, soft robotics, and in-sensor computing. Ion-conducting polymers, by uniquely combining brain-like ionic signaling with soft-matter versatility, are expected to play a central role in the next generation of intelligent, bio-integrated systems.</p>