Bioprinting has emerged in recent years as an attractive method for creating 3-D tissues and organs in the laboratory, and therefore is a promising technology in a number of regenerative medicine applications. It has the potential to (i) create fully functional replacements for damaged tissues in patients, and (ii) rapidly fabricate small-sized human-based tissue models, or organoids, for diagnostics, pathology modeling, and drug development. A number of bioprinting modalities have been explored, including cellular inkjet printing, extrusion-based technologies, soft lithography, and laser-induced forward transfer. Despite the innovation of each of these technologies, successful implementation of bioprinting relies heavily on integration with compatible biomaterials that are responsible for supporting the cellular components during and after biofabrication, and that are compatible with the bioprinting device requirements. In this review, we will evaluate a variety of biomaterials, such as curable synthetic polymers, synthetic gels, and naturally derived hydrogels. Specifically we will describe how they are integrated with the bioprinting technologies above to generate bioprinted constructs with practical application in medicine.