We report a detailed experimental study of the structure and dynamics of glassy states in hard spheres with short-range attraction. The system is a suspension of nearly hard-sphere colloidal particles and nonadsorbing linear polymer which induces a depletion attraction between the particles. Observation of crystallization reveals a reentrant glass transition. Static light scattering shows a continuous change in the static structure factors upon increasing attraction. Dynamic light scattering results, which cover 11 orders of magnitude in time, are consistent with the existence of two distinct kinds of glasses, those dominated by interparticle repulsion and caging, and those dominated by attraction. Samples close to the “A3 point” predicted by mode coupling theory for such systems show very slow, logarithmic dynamics.