A history of the development of selective laser spectroscopy is presented, beginning with a pioneering work by Yu. V. Denisov and V. A. Kizel in 1967, who were the first to demonstrate the possibility of removing the inhomogeneous broadening of luminescence spectra of impurity ions in glasses upon monochromatic resonance excitation. Selective excitation of optical centers can be achieved due to existence of zero-phonon transitions corresponding to narrow homogeneous zero-phonon lines in the spectra of impurity centers in solids, which are hidden in broad inhomogeneous optical bands upon usual nonselective excitation. The fundamentals of zero-phonon transition spectroscopy are considered and the mechanism of removing the inhomogeneous broadening of optical spectra of ions and molecules in crystals and amorphous solids under selective laser excitation of luminescence and persistent hole burning in absorption spectra is presented in detail. Various applications of selective laser spectroscopy for fundamental and applied studies are discussed.