Desiccation-tolerant (orthodox) seeds can survive in the dry state for considerable periods and so can be stored successfully at low water content and subzero temperatures. Orthodox seeds possess a variety of protective processes and mechanisms that confer desiccation tolerance, important among them being metabolic shutdown and intracellular dedifferentiation. In contrast, desiccation-sensitive (recalcitrant) seeds cannot tolerate water loss and so cannot be stored using conventional seed bank conditions. Particularly with respect to storage, recalcitrant seeds do not undergo intracellular dedifferentiation nor any significant metabolic shutdown. Embryos of recalcitrant seeds remain metabolically active, with little or no reduction in extent of the extensive intracellular membranes. At the water content at which they are shed, with the ongoing metabolism in recalcitrant seeds, developmental phenomena grade imperceptibly into those associated with germination. Thus, recalcitrant seeds can be stored intact only until germination is initiated, which can range from a few days to several months, depending on species. Mild drying to inhibit germination in storage (subimbibed storage) leads to more rapid loss of viability. The only feasible method for long-term storage of germplasm of recalcitrant-seeded species is cryopreservation, but this requires partial drying to prevent ice crystal damage. However, the response to drying depends on the drying rate: slow drying induces viability loss at high water contents, whereas material dried rapidly can survive (in the short term) to water contents low enough to permit vitrification of the remaining intracellular water rather than the formation of ice crystals, if cooling rates are rapid enough. Recalcitrant seeds are almost invariably too large to permit the rates of drying and cooling required for vitrification, and so excised embryonic axes are generally the explants of choice. This review highlights how the physiology of recalcitrant seeds impacts on attempts to cryopreserve the excised embryonic axes/embryos.