Microwave discharges (MD) are widely used as a source of non-equilibrium low pressure plasma for different applications. This paper reviews the methods of microwave plasma generation at pressures from 10 −2 approximately to 30 kPa with centimeter-millimeter wavelength microwaves on the basis of scientific publications since 1950 up to the present. The review consists of 16 sections. A general look at MDs and their application is given in the introduction, together with a description of a typical block-schema of the microwave plasma generator, classification of MD, and attractive features of MD. Sections 2-12 describe the different methods of microwave plasma generators on the basis of cavity and waveguide discharges, surface and slow wave discharges, discharges with distributed energy input, initiated and surface discharges, discharges in wave beams, discharges with stochastically jumping phases of microwaves, discharges in an external magnetic field and discharges with a combination of microwave field and dc and RF fields. These methods provide the possibility of producing nonequilibriun high density plasma in small and large chambers for many applications. Plasma chemical activity of nonequilibrium microwave plasma is analyzed in section 13. A short consideration of the history and status of the problem is given. The main areas of microwave plasma application are briefly described in section 14. Non-uniformity is the inherent property of the majority of electrical discharges and MDs are no exception. Peculiarities of physical-chemical processes in strongly non-uniform MDs are demonstrated placing high emphasis on the influence of small noble gas additions to the main plasma gas (section 15). The review is illustrated by 80 figures. The list of references contains 350 scientific publications.