The efficient use of energy is a prerequisite for the sustainable development of modern society. It requires increasing heat recuperation in various energy-reliant systems, which is possible with heat transfer devices of intensive action, operating in conditions of limited space for installation and material availability for their production. This is achieved by heat exchangers with mini- and micro-channels, regarded as the next generation of heat transfer equipment. A survey of publications on heat transfer and pressure losses in mini- and microchannels is presented, with focus on their thermal-hydraulic performance. It includes straight channels of various cross-sectional forms, channels with enhanced heat transfer for electronic cooling, additively manufactured microchannels, crisscross flow channels of microturbine recuperators, and plate heat exchangers. A novel Micro Heat Factor for the comparison of mini- and microchannels thermal-hydraulic performance is derived. For the detailed estimation of channel performance in specified process conditions, accounting for the differences in hydraulic diameters, the equation for optimal fluid velocity is proposed. The comparison of thermal-hydraulic performance for different types of mini- and micro channels is performed, and the possibilities of their use in heat exchangers at specific applications are discussed, followed by directions of future studies.