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Programmable photonics play a crucial role in many emerging applications, from optical accelerators for machine learning to quantum information technologies. Conventionally, photonic systems are tuned by mechanisms such as the thermo-optic effect, free carrier dispersion, the electro-optic effect, or micro-mechanical movement. Although these physical effects allow either fast (>100 GHz) or large contrast (>60 dB) switching, their high static power consumption is not optimal for programmability, which requires only infrequent switching and has a long static time. Non-volatile materials, such as phase-change materials, ferroelectrics, vanadium dioxide, and memristive metal oxide materials, can offer an ideal solution thanks to their reversible switching and non-volatile behavior, enabling a truly “set-and-forget” programmable unit with no static power consumption. In recent years, we have indeed witnessed the fast adoption of non-volatile materials in programmable photonic systems, including photonic integrated circuits and free-space meta-optics. Here, we review the recent progress in the field of programmable photonics, based on non-volatile materials. We first discuss the material’s properties, operating mechanisms, and then their potential applications in programmable photonics. Finally, we provide an outlook for future research directions. The review serves as a reference for choosing the ideal material system to realize non-volatile operation for various photonic applications.