This chapter presents a comprehensive exploration of Josephson junction (JJ) and superconducting quantum interference device (SQUID)-based superconducting memories, focusing on their critical role in advancing quantum computing and cryogenic electronics. JJs, fundamental to superconducting circuits, exhibit non-linear current–voltage characteristics that can be harnessed for memory storage through precise control of the superconducting phase difference. SQUIDs, which consist of a loop of superconducting material interrupted by one or more JJs, extend these capabilities by enabling ultra-sensitive magnetic flux measurements and phase control, making them ideal candidates for memory applications. This chapter begins by explaining the principles of operation of JJs and then discusses various memory designs, including vortex transition-based, SQUID-based DC-powered, and small JJ array-based memory cells. The chapter details the design principles, operational mechanisms, and performance metrics of these memory systems. Additionally, it discusses the existing challenges such as large cell areas, flux trapping, and fabrication complexities. By examining these factors, the chapter underscores the advancements and ongoing challenges in developing high-performance superconducting memories for cryogenic applications.