Human-machine interaction (HMI) technology has undergone significant advancements in recent years, enabling seamless communication between humans and machines. Its expansion has extended into various emerging domains, including human healthcare, machine perception, and biointerfaces, thereby magnifying the demand for advanced intelligent technologies. Neuromorphic computing, a paradigm rooted in nanoionic devices that emulate the operations and architecture of the human brain, has emerged as a powerful tool for highly efficient information processing. This paper delivers a comprehensive review of recent developments in nanoionic device-based neuromorphic computing technologies and their pivotal role in shaping the next-generation of HMI. Through a detailed examination of fundamental mechanisms and behaviors, the paper explores the ability of nanoionic memristors and ion-gated transistors to emulate the intricate functions of neurons and synapses. Crucial performance metrics, such as reliability, energy efficiency, flexibility, and biocompatibility, are rigorously evaluated. Potential applications, challenges, and opportunities of using the neuromorphic computing technologies in emerging HMI technologies, are discussed and outlooked, shedding light on the fusion of humans with machines.