We have systematically investigated the phase diagram of clay particles in water in order to understand the relation between the local and macroscopic properties and the structure of clay suspensions. We focused in particular on sodium Cloisite (CNa) particles at concentrations from 1 wt% to 4 wt%, and at an extended range of ionic strengths (10-5 to 10-2 M NaCl). The suspensions have been characterized using rheology and a combination of scattering techniques (neutrons, x-rays, light). We were able to demonstrate the existence of a liquid cluster phase at low clay and intermediate salt concentration, and obtained new insight into the nature of the solid-like dispersions at low and high ionic strength. In particular we were able to unambiguously demonstrate the existence of an arrested phase at low concentrations and ionic strength that corresponds to the Wigner glass predicted on theoretical grounds for such systems.