Critical-sized bone defects and articular cartilage injuries resulting from trauma, osteonecrosis, or age-related degeneration can be often non-healed by physiological repairing mechanisms, thus representing a relevant clinical issue due to a high epidemiological incidence rate. Novel tissue-engineering approaches have been proposed as an alternative to common clinical practices. This cutting-edge technology is based on the combination of three fundamental components, generally referred to as the tissue-engineering triad: autologous or allogenic cells, growth-stimulating factors, and a scaffold. Three-dimensional polymer networks are frequently used as scaffolds to allow cell proliferation and tissue regeneration. In particular, cryogels give promising results for this purpose, thanks to their peculiar properties. Cryogels are indeed characterized by an interconnected porous structure and a typical sponge-like behavior, which facilitate cellular infiltration and ingrowth. Their composition and the fabrication procedure can be appropriately tuned to obtain scaffolds that match the requirements of a specific tissue or organ to be regenerated. These features make cryogels interesting and promising scaffolds for the regeneration of different tissues, including those characterized by very complex mechanical and physical properties, such as bones and joints. In this review, state-of-the-art fabrication and employment of cryogels for supporting effective osteogenic or chondrogenic differentiation to allow for the regeneration of functional tissues is reported. Current progress and challenges for the implementation of this technology in clinical practice are also highlighted.