Published data on spectroscopic characteristics of saturable absorbers based on crystals doped with tetrahedrally coordinated transition-metal ions (Cr 2+ , Cr 4+ , Cr 5+ , V 3+ , Cr 2+ , Fe 2+ ) in addition to their use as passive Q-switches for solid-state lasers emitting in the visible and near-infrared regions are reviewed.Introduction. The use of saturable absorbers (SA) as passive Q-switches (PS) in solid-state lasers is an effective method for generating nanosecond and subnanosecond light pulses. This method differs favorably from active control of laser cavity gain by the lack of mechanical perturbations of the optical devices, additional sources of power supply, and external electrical control circuits. This simplifies the construction and operation of the laser and reduces its cost. Compact solid-state mini-lasers and ultra-small lasers (so-called microchip lasers) can be fabricated if PS are used.A SA is an optical material for which the transmission increases with increasing power density of the incident radiation. The SA should satisfy several requirements in order to be used as a PS. First of all this applies to SA characteristics at the laser operating wavelength such as absorption saturation energy density, coefficient of residual absorption in the fully bleached state, bleaching rise and fall time, and optical destruction threshold. The requirements for their absolute values depend on the spectroscopic properties of the lasing medium (LM) and the laser cavity parameters.In most instances with certain exceptions, SA based on tetrahedrally coordinated (TC) transition-metal ions of the iron group have bleaching relaxation times that are longer than the generation time of the laser pulses obtained using them. Such SA are usually called slowly relaxing. Relaxation processes leading to a restoration of their initial absorption can be ignored in analyzing their operation in a laser. In the simplest instance (if a four-level diagram is used for the spectroscopic model of the SA), the criterion for SA functioning as a PS is written [1-8]: