  We introduce a microscopically realistic model of a physical gel and use
computer simulations to study its static and dynamic properties at thermal
equilibrium. The phase diagram comprises a sol phase, a coexistence region
ending at a critical point, a gelation line determined by geometric
percolation, and an equilibrium gel phase unrelated to phase separation. The
global structure of the gel is homogeneous, but the stress is supported by a
fractal network. The gel dynamics is highly heterogeneous and we propose a
theoretical model to quantitatively describe dynamic heterogeneity in gels. We
elucidate several differences between the dynamics of gels and that of
glass-formers.
