Calcium phosphate (CaP) bioceramics are widely used in the field of bone regeneration, both in orthopedics and in dentistry, due to their good biocompatibility, osseointegration and osteoconduction. The aim of this article is to review the history, structure, properties and clinical applications of these materials, whether they are in the form of bone cements, paste, scaffolds, or coatings. Major analytical techniques for characterization of CaPs, in vitro and in vivo tests, and the requirements of the US Food and Drug Administration (FDA) and international standards from CaP coatings on orthopedic and dental endosseous implants, are also summarized, along with the possible effect of sterilization on these materials. CaP coating technologies are summarized, with a focus on electrochemical processes. Theories on the formation of transient precursor phases in biomineralization, the dissolution and reprecipitation as bone of CaPs are discussed. A wide variety of CaPs are presented, from the individual phases to nano-CaP, biphasic and triphasic CaP formulations, composite CaP coatings and cements, functionally graded materials (FGMs), and antibacterial CaPs. We conclude by foreseeing the future of CaPs.