This chapter explores the development and application of superconducting memristor-based memory technologies, with a focus on their integration into superconducting circuits for quantum computing and other cryogenic environments. Superconducting memristors, leveraging the hysteretic behavior of resistance states, offer a novel approach to non-volatile memory in superconducting systems. By utilizing high resistance (HRS) and low resistance states (LRS) to represent binary logic, these devices enable the design of memory cells that are both energy-efficient and compatible with the low-temperature operation required in quantum computing. The chapter details the underlying mechanisms of superconducting memristors, including their current-driven read/write operations, and discusses their potential advantages over conventional memory technologies. Additionally, the integration of superconducting memristors with existing superconducting technologies, such as Josephson junctions and superconducting quantum interference devices (SQUIDs), is examined. The chapter concludes with an outlook on future research directions and the potential for superconducting memristor-based memory to revolutionize data storage in quantum computing and other advanced cryogenic applications.