Dynamics and domain walls: Is the ''landscape paradigm'' instructive?

General questions concerning the dynamics of systems with many degrees of freedom are discussed, focussing on approach to equilibrium in simple statistical mechnical models. The contrasts between the behavior of systems with short-range interactions and mean-field pictures in terms of energy ''landscapes'' are emphasized. It is shown how much of the behavior of systems with short-range interactions can be described in terms of domain walls and their dynamics. Simple Ising magnetic models, both ferromagnets and spin glasses, are used as a paradigm.