Color centers in diamond, silicon carbide, and related materials have recently emerged as one of the most promising platforms for quantum technology applications. These optically active point defects in the crystal lattice demonstrate outstanding optical and spin properties at room and even higher temperatures, which can hardly be achieved using other quantum systems. For a long time, the host material was considered only as a mechanical carrier of color centers, and the fact that it is a semiconductor and, therefore, can contain high densities of electrons and holes, was ignored. However, recent studies have demonstrated that color centers can exchange electrons and holes with the valence or conduction bands of the host material, which enables novel functionalities, ranging from ultrabright electrically driven single-photon sources to protected quantum memories. This review summarizes recent advances in understanding this interaction.