The introductory section of the review lists the main problems which can be solved by laser spectroscopy methods: 1) achievement of the ultimate resolving power; 2) suppression of the Doppler broadening in the gaseous phase; 3) attainment of the ultimate sensitivity in spectroscopic analysis of atoms and molecules; 4) investigation of the spectra and relaxation originating from excited states; 5) remote spectroscopic analysis; 6) local spectroscopic analysis. This is followed by a section which presents the current status of tunable lasers, including dye solution, semiconductor, and high-pressure molecular gas lasers, parametric oscillators, and spin-flip lasers; nonlinear frequency conversion methods are also considered. Next, a more detailed analysis is made of the following types of laser spectroscopy: 1) linear spectroscopy (external absorption, intraresonator absorption, optoacoustic, and fluorescence methods, and a comparison of these methods); 2) nonlinear spectroscopy free of the Doppler broadening (absorption saturation, two-photon, and particle ``trapping'' method; a comparison of the sensitivity and resolution of these methods; new spectroscopic information; precision spectroscopy); 3) Raman (spontaneous, inverse, and active) spectroscopy; 4) two-photon absorption spectroscopy; 5) selective detection of small amounts of atoms and molecules (local and remote detection); spectroscopy of excited states, high states of atoms, and vibrattonal states of molecules; picosecond laser spectroscopy of excited molecules).