  We use dynamic light scattering and numerical simulations to study the
approach to equilibrium and the equilibrium dynamics of systems of colloidal
hard spheres over a broad range of density, from dilute systems up to very
concentrated suspensions undergoing glassy dynamics. We discuss several
experimental issues (sedimentation, thermal control, non-equilibrium aging
effects, dynamic heterogeneity) arising when very large relaxation times are
measured. When analyzed over more than seven decades in time, we find that the
equilibrium relaxation time, tau_alpha, of our system is described by the
algebraic divergence predicted by mode-coupling theory over a window of about
three decades. At higher density, tau_alpha increases exponentially with
distance to a critical volume fraction phi_0 which is much larger than the
mode-coupling singularity. This is reminiscent of the behavior of molecular
glass-formers in the activated regime. We compare these results to previous
work, carefully discussing crystallization and size polydispersity effects. Our
results suggest the absence of a genuine algebraic divergence of tau_alpha in
colloidal hard spheres.
