Hard tissues (e.g., bone, enamel, dentin) in vertebrates perform various and different functions, from sustaining the body to haematopoiesis. Such complex and hierarchal tissue is actually a material composite whose static and dynamic properties are controlled by the subtle physical and chemical interplay between its components, collagen (main organic part) and hydroxylapatite-like mineral. The knowledge needed to fully understand the properties of bony and dental tissues and to develop specific applicative biomaterials (e.g., fillers, prosthetics, scaffolds, implants, etc.) resides mostly at the atomic scale. Among the different methods to obtains such detailed information, atomistic computer simulations (in silico) have proven to be both corroborative and predictive tools in this subject. The authors have intensively worked on quantum mechanical simulations of bioapatite and the present work reports a detailed review addressed to the crystal-chemical, physical, spectroscopic, mechanical, and surface properties of the mineral phase of bone and dental tissues. The reviewed studies were conducted at different length and time scales, trying to understand the features of hydroxylapatite and biological apatite models alone and/or in interaction with simplified collagen-like models. The reported review shows the capability of the computational approach in dealing with complex biological physicochemical systems, providing accurate results that increase the overall knowledge of hard tissue science.