Memristors, as transformative electronic devices designed to transcend the von Neumann architecture, enable the physical unification of information storage and computation, thereby offering a foundational hardware pathway toward energy-efficient, brain-inspired computing. Their intrinsic analog resistive switching, non-volatility, and history-dependent learning capabilities allow them to natively implement in-memory computing and emulate synaptic plasticity, addressing the critical bottlenecks of energy and speed in conventional systems. Notably, the evolution from electrically controlled memristors to optoelectronic memristors marks a paradigm shift from pure computing to integrated sensing-processing, opening new dimensions for high-speed, parallel, and adaptive signal processing. In recent years, significant progress has been made in the development of memristor-based neuromorphic vision and tactile systems, on-chip signal processors, and dynamic trajectory trackers, demonstrating their potential in edge intelligence, adaptive robotics, and real-time perceptual tasks. This review systematically summarizes the latest advances in memristor technology, providing a comprehensive analysis of their operating mechanisms, material and structural innovations, and cutting-edge applications in neuromorphic perception and computing. Furthermore, it discusses the key challenges and future directions for the development and integration of memristor-based systems in the post-von Neumann era.