  The kinetic properties of relativistic quark-gluon and electron-photon
plasmas are described in the weak coupling limit. The troublesome Rutherford
divergence at small scattering angles is screened by Debye screening for the
longitudinal or electric part of the interactions. The transverse or magnetic
part of the interactions is effectively screened by Landau damping of the
virtual photons and gluons transferred in the QED and QCD interactions
respectively. Including screening a number of transport coefficients for QCD
and QED plasmas can be calculated to leading order in the interaction strength,
including rates of momentum and thermal relaxation, electrical conductivity,
viscosities, flavor and spin diffusion of both high temperature and degenerate
plasmas. Damping of quarks and gluons as well as color diffusion in quark-gluon
plasmas is, however, shown not to be sufficiently screened and the rates
depends on an infrared cut-off of order the ``magnetic mass", $m_{\rm mag}\sim
g^2 T$.
