Laponite dispersions in water, at moderate ionic strength and high pH, are thixotropic: depending on previous history, they can be fluids or gels. The mechanisms of the fluid-gel and gel-fluid transitions have been examined through ionic analysis of the aqueous phase, static light, and small-angle neutron scattering, rheological experiments, and centrifugation. The results indicate that the particles attract each other in edge-to-face configurations. These attractions cause the particles to gather in microdomains, which subsequently associate to form very large fractal superaggregates, containing all the particles in the dispersion. A gel state is obtained when the network of connections is macroscopic. This network is destroyed by the application of sufficient strain, but it heals at rest. The addition of peptizers weakens the edge-to-face attractions, and makes the healing times much slower.