  I try to explain some recent progress in understanding the non-perturbative
dynamics of hot non-Abelian gauge theories. The non-perturbative physics is due
to soft spatial momenta $|\vec{p}|\sim g^2 T$ where $g$ is the gauge coupling
and $T$ is the temperature. An effective theory for the soft field modes is
obtained by integrating out the field modes with momenta of order $T$ and of
order $g T$ in a leading logarithmic approximation. In this effective theory
the time evolution of the soft fields is determined by a local Langevin-type
equation. This effective theory determines the parametric form of the rate for
hot electroweak baryon number violation as $\Gamma = \kappa g^{10} \log(1/g)
T^4$. The non-perturbative coefficient $\kappa$ is independent of the gauge
coupling and it can be computed by solving the effective equations of motion on
a lattice.
