This article reviews the current status of the theory of vibrational relaxation in gases and its applications to the theory of molecular lasers. We discuss relaxation of the vibrational energy of diatomic and polyatomic molecules as represented by harmonic-oscillator models. The vibrational kinetics in a system of anharmonic oscillators is analyzed in detail. We treat quasi-steady-state population distributions of vibrational levels that arise under substantially non-equilibrium conditions, both in a singlecomponent molecular system and in gas mixtures. We discuss relaxation that proceeds in the presence of sources of vibrationally-excited molecules: infrared resonance radiation, recombination, and dissociation; in particular, we analyze the process of non-equilibrium dissociation at low gas temperatures. We discuss from a unified standpoint based on vibrational kinetics the working mechanisms of lasers using vibrational-rotational transitions in diatomic and polyatomic molecules with various means of excitation (electrical, chemical, and gas-dynamic).