Hydrogels are an important class of highly hydrated polymers that are widely investigated for potential use in soft tissue engineering. Generally, however, hydrogels lack the ability to mineralize, preventing the formation of chemical bonds with hard tissues such as bone. A recent trend in tissue engineering involves the development of hydrogels that possess the capacity to mineralize. The strategy that has attracted most interest has been the incorporation of inorganic phases such as calcium phosphate ceramics and bioglasses into hydrogel matrices. These inorganic particles act as nucleation sites that enable further mineralization, thus improving the mechanical properties of the composite material. A second route to create nucleation sites for calcification of hydrogels involves the use of features from the physiological mineralization process. Examples of these biomimetic mineralization strategies include (1) soaking of hydrogels in solutions that are saturated with respect to calcium phosphate, (2) incorporation of enzymes that catalyze deposition of bone mineral, and (3) incorporation of synthetic analogues to matrix vesicles that are the initial sites of biomineralization. Functionalization of the polymeric hydrogel backbone with negatively charged groups is a third mechanism to promote mineralization in otherwise inert hydrogels. This review summarizes the main strategies that have been developed in the past decade to calcify hydrogel matrices and render these hydrogels suitable for applications in bone regeneration.