The evaluation of hydrodynamic transport coefficients in relativistic field theory, and the emergence of an effective kinetic theory description, is examined. Even in a weakly-coupled scalar field theory, interesting subtleties arise at high temperatures where thermal renormalization effects are important. In this domain, a kinetic theory description in terms of the fundamental particles ceases to be valid, but one may derive an effective kinetic theory describing excitations with temperature dependent properties. While the shear viscosity depends on the elastic scattering of typical excitations whose kinetic energies are comparable to the temperature, the bulk viscosity is sensitive to particle non-conserving processes at small energies. As a result, the shear and the bulk viscosities have very different dependence on the interaction strength and temperature, with the bulk viscosity providing an especially sensitive test of the validity of an effective kinetic theory description.

27 pages, revtex format, 5 postscript figures included using epsf.sty