The effect of electric and magnetic plasma microfields on elementary many-body processes in plasmas is considered. As detected first by Inglis and Teller in 1939, the electric microfield controls several elementary processes in plasmas as transitions, line shifts and line broadening. We concentrate here on the many-particle processes ionization, recombination, and fusion and study a wide area of plasma parameters. In the first part the state of art of investigations on microfield distributions is reviewed in brief. In the second part, various types of ionization processes are discussed with respect to the influence of electric microfields. It is demonstrated that the processes of tunnel and rescattering ionization by laser fields as well as the process of electron collisional ionization may be strongly influenced by the electric microfields in the plasma. The third part is devoted to processes of microfield action on fusion processes and the effects on three-body recombination are investigated. It is shown that there are regions of plasma densities and temperatures, where the rate of nuclear fusion is accelerated by the electric microfields. This effect may be relevant for nuclear processes in stars. Further, fusion processes in ion clusters are studied. Finally we study in this section three-body recombination effects and show that an electric microfield influences the three-body electron-ion recombination via the highly excited states. In the fourth part, the distribution of the magnetic microfield is investigated for equilibrium, nonequilibrium, and non-uniform magnetized plasmas. We show that the field distribution in a neutral point of a non-relativistic ideal equilibrium plasma is similar to the Holtsmark distribution for the electrical microfield. Relaxation processes in nonequilibrium plasmas may lead to additional microfields. We show that in turbulent plasmas the broadening of radiative electron transitions in atoms and ions, without change of the principle quantum number, may be due to the Zeeman effect and may exceed Doppler and Stark broadening as well. Further it is shown that for optical radiation the effect of depolarization of a linearly polarized laser beams propagating through a magnetized plasma may be rather strong.