We present a review of results from study of the nonlinear optical properties and relaxation processes in lead chalcogenide quantum dots embedded in glass matrices of various compositions, and also designs for bleachable media based on these materials for Q-switched and mode-locked solid-state lasers in the near IR range. We consider the conditions which should be satisfied by the spectroscopic characteristics of saturable absorbers for realization of passive Q-switching and mode-locking in solid-state lasers.Introduction. Nanometer-sized semiconductor particles (quantum dots (QDs)) are among systems with pronounced quantum effects, caused by confinement of the motion of the electrons and holes by the finite dimensions of the nanoparticle [1][2][3][4]. If the dimensions of the quantum dot are comparable with the Bohr exciton radius in a bulk semiconductor, then we observe a shift of the optical absorption edge of the quantum dot toward higher energies relative to the bandgap width of the bulk semiconductor. To a first approximation, the magnitude of this shift is inversely proportional to the square of the quantum dot radius. Furthermore, the quantum dot absorption spectrum has structure: individual bands appear due to splitting of the valence band and the conduction band into individual energy levels, between which there are certain optical transitions with selection rules. As a result, it becomes possible to monotonically shift the quantum dot absorption edge toward shorter wavelengths, starting from the wavelength corresponding to the bandgap width of the semiconductor compound. Thus semiconductors with a relatively narrow bandgap, in particular lead chalcogenides, make it possible to shift the absorption edge within practically the entire near IR region of the spectrum, by varying the size of the quantum dot. The effect of an increase in transmission (bleaching) in the region of the quantum dot absorption bands upon resonant interaction with an intense light beam allows us to use quantum dots as bleachable media (saturable absorbers) to control the temporal parameters of emission from laser systems.Bleachable media, using the effect of saturation of optical absorption, have become widely used to obtain high-power light pulses of short/ultrashort duration in Q-switched and mode-locked solid-state lasers emitting in the near IR region of the spectrum. Using such laser pulses provides broad possibilities for treatment of materials, information transfer, ranging, monitoring for occurrence of industrial processes, environmental monitoring, biomedical diagnostics, laser surgery and therapy, and also in science (especially in nonlinear optics and laser spectroscopy). Practical application requires laser systems that operate reliably, are easy to service, compact, and low-cost. A solid-state bleachable medium as a component of a laser system sufficiently meets the indicated requirements. This component is usually a plate or film (on a substrate) made from a solid material, and does not require any external mechanical...