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Screening and charging of a grain in a weakly ionized plasma background are studied within the drift-diffusion approximation. The computations evidence that the account of grain charging results in a distinct qualitative change in the screened field as compared to the thermodynamically equilibrium case of a grain with a constant charge. The stationary grain charge as well as the field within the sheath around the grain are shown to be almost independent of the type of boundary conditions (for relatively low ionization rates and small grain sizes), whereas the asymptotical behavior of the effective field is rather sensitive to them.

The first principles of statistical mechanics are used to formulate the basic points of kinetic theory of dusty plasmas. Equations for microscopic phase densities of plasma particles and grains are derived with regard for electron and ion collection by dust particles and elastic contact collisions between grains. The Bogolyubov–Born–Green–Kirkwood–Yvon hierarchy is generalized to the case of dusty plasmas and used to derive kinetic equations, taking into account elastic and inelastic particle collisions. An example of such an equation is presented and applied to the calculations of stationary grain velocity and charge grain distributions. The results of Monte Carlo studies of a strongly coupled dusty plasma are also presented. Microscopic simulations of critical behavior of a dusty plasma with regard for the discrete nature of the plasma subsystem are performed. The effect of nonlinear screening of dust particles on the dusty crystal formation is considered as well.

Recent important results are briefly presented concerning the screening of high-Z impurities in colloidal plasmas. The review focuses on the phenomenon of nonlinear screening and its effects on the structure of colloidal plasmas, the role of trapped ions in grain screening, and the effects of strong collisions in the plasma background. It is shown that the above effects may strongly modify the properties of the grain screening giving rise to considerable deviations from the conventional Debye-Hückel theory as dependent on the physical processes in the plasma background.