  We review the non-zero temperature relaxational dynamics of quantum systems
near a zero temperature, second-order phase transition. We begin with the
quantum Ising chain, for which universal and exact results for the relaxation
rates can be obtained in all the distinct limiting regimes of the phase
diagram. Next, we describe the crossovers in the electron spectral function
near a transition involving a change in the pairing symmetry of BCS
superconductors in two dimensions. Finally, we consider dynamic spin models
which may provide a mean-field description of magnetic ordering transitions in
the heavy fermion compounds.
