Long-horizon robotic tasks expose a fundamental limitation of current Vision-Language-Action (VLA) models because their restricted temporal context pre-vents effective accumulation and reuse of past experiences. As a result, memory has become a fundamental component for enabling embodied agents to perform long-horizon reasoning and adaptive decision-making. This survey presents a systematic taxonomy of VLA memory mechanisms based on memory scope and persistence, categorizing existing approaches into five representative paradigms and one emerging frontier. Based on this taxonomy, we compare representative VLA memory systems in terms of memory characteristics, architectural com-plexity, and open-source maturity, revealing a clear trade-off in which increasing architectural complexity is generally accompanied by decreasing open-source ma-turity. Finally, we discuss the key challenges in building full-lifecycle memory systems, including efficient memory management and lifelong knowledge evolu-tion. Overall, this survey provides a unified perspective on memory architectures for VLA agents and offers insights into the development of lifelong embodied in-telligence.