Shear thickening of low-concentration solutions of wormlike micelles is investigated using simultaneous rheological and visualization measurements. Shear-induced. structures (SISs) are directly visualized in transparent Couette cells using a laser light scattering technique similar to dark-field microscopy. From these measurements, four different regimes of behavior are identified. In regime I, which occurs below a critical shear stress alpha(c), the shear rate increases monotonically with stress and no shear thickening or SISs are observed. In regime II, which occurs for stresses greater than sigma(c) but less than alpha(s), SISs nucleate inhomogeneously and grow from the inner cylinder of the Couette cell. In this regime, the steady state shear rate initially decreases with increasing stress and then increases again as the stress is raised. The steady state in regime II is characterized by two coexisting states separated by a cylindrical interface ( concentric with the Couette cylinders). Near the inner cylinder, viscous SISs are observed, while near the outer cylinder, a much less viscous fluid similar to the original micellar solution is observed. The steady state in regime II is observed only under conditions of controlled stress. In regime III, which occurs for stresses above sigma(s) but below sigma(f), SISs nucleate homogeneously throughout the shear cell and appear to fill the gap. Regime IV is characterized by the fracture of SIS and is observed at sigma(f). The shear-thickening transition bears many similarities to a phase transition as opposed to a simple hydrodynamic instability.