Recently, the favorable electrical properties of biomaterials have been acknowledged as crucial for various medical applications, including both bone healing and growth processes. This review will specifically concentrate on calcium phosphate (CaP)-based bioceramics, with a notable emphasis on hydroxyapatite (HA), among the diverse range of synthetic biomaterials. HA is currently the subject of extensive research in the medical field, particularly in dentistry and orthopedics. The existing literature encompasses numerous studies exploring the physical–chemical, mechanical, and biological properties of HA-based materials produced in various forms (i.e., powders, pellets, and/or thin films) using various physical and chemical vapor deposition techniques. In comparison, there is a relative scarcity of research on the electrical and dielectric properties of HA, which have been demonstrated to be essential for understanding dipole polarization and surface charge. It is noteworthy that these electrical and dielectric properties also offer valuable insights into the structure and functioning of biological tissues and cells. In this respect, electrical impedance studies on living tissues have been performed to assess the condition of cell membranes and estimate cell shape and size. The need to fill the gap and correlate the physical–chemical, mechanical, and biological characteristics with the electrical and dielectric properties could represent a step forward in providing new avenues for the development of the next-generation of high-performance HA-doped biomaterials for future top medical applications. Therefore, this review focuses on the electrical and dielectric properties of HA-based biomaterials, covering a range from powders and pellets to thin films, with a particular emphasis on the impact of the various dopants used. Therefore, it will be revealed that each dopant possesses unique properties capable of enhancing the overall characteristics of the produced structures. Considering that the electrical and dielectric properties of HA-based biomaterials have not been extensively explored thus far, the aim of this review is to compile and thoroughly discuss the latest research findings in the field, with special attention given to biomedical applications.