Calcium phosphates (CaPs) and their substituted derivatives encompass a large number of compounds with a vast presence in nature that have aroused a great interest for decades. In particular, hydroxyapatite (HAp, Ca10(OH)2(PO4)6) is the most abundant CaP mineral and is significant in the biological world, at least in part due to being a major compound in bones and teeth. HAp exhibits excellent properties, such as safety, stability, hardness, biocompatibility, and osteoconductivity, among others. Even some of its drawbacks, such as its fragility, can be redirected thanks to another essential feature: its great versatility. This is based on the compound’s tendency to undergo substitutions of its constituent ions and to incorporate or anchor new molecules on its surface and pores. Thus, its affinity for biomolecules makes it an optimal compound for multiple applications, mainly, but not only, in biological and biomedical fields. The present review provides a chemical and structural context to explain the affinity of HAp for biomolecules such as proteins and nucleic acids to generate hybrid materials. A size-dependent criterium of increasing complexity is applied, ranging from amino acids/nucleobases to the corresponding macromolecules. The incorporation of metal ions or metal complexes into these functionalized compounds is also discussed.