Hard spheres have been used to model many different systems in condensed matter. Amorphous packings have attracted a lot of interest as theoretical models for glasses. We will review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. Replica theory relies on approximations and certain assumptions that will be elucidated in this paper. The aim of this paper is to identify a class of amorphous packings that might be described using equilibrium statistical mechanics, that is, in a static framework. These packings will be defined as the infinite pressure limit of glassy states of hard spheres.