Memristors stand out as the most promising candidates for non-volatile memory and neuromorphic computing due to their unique properties. A crucial strategy for optimizing memristor performance lies in voltage modulation, which is essential for achieving ultra-low power consumption in the nanowatt range and ultra-low energy operation below the femtojoule level. This capability is pivotal in overcoming the power consumption barrier and addressing the computational bottlenecks anticipated in the post-Moore era. However, for brain-inspired computing architectures that leverage high-density integrated memristor arrays, it is imperative to consider key device stability parameters, including the on/off ratio, high-speed response, retention time, and durability. Achieving efficient and stable ion/electron transport under low electric fields to develop low-voltage, high-performance memristors operating below 1 V is critical for advancing energy-efficient neuromorphic computing systems. This review provides a comprehensive overview of recent advancements in low-voltage memristors for neuromorphic computing. Firstly, it begins by elucidating the mechanisms that govern low-voltage memristor operation, such as electrochemical metallization and anion migration. These mechanisms play a pivotal role in determining the overall performance and reliability of memristors under low-voltage conditions. Secondly, the review then systematically examines the advantages of various material systems employed in low-voltage memristors, including transition metal oxides, two-dimensional materials, and organic materials. Each material system offers distinct benefits, such as low ion activation energy, appropriate defect density etc., which are critical for optimizing memristor performance at low operating voltages. Thirdly, the review consolidates strategies for achieving low-voltage memristors through advanced materials engineering, doping engineering, and interface engineering. Moreover, the potential applications of low-voltage memristors in neuromorphic function simulation and neuromorphic computing are discussed. Finally, the current problems of low-voltage memristors are discussed, especially the stability issues and limited application scenarios. Future research directions are proposed, focusing on exploring new material systems and physical mechanisms that could be integrated into device design to achieve higher-performance low-voltage memristors.