Reverse micelles in the AOT/water/isooctane system, at various water contents (W(0)), were studied using rheometry and small angle X-ray scattering (SAXS) experiments under static conditions and under shear. The SAXS analysis confirmed the spherical shape of the micelles at low water content and revealed a transition into elongated micelles at higher water content. A population of spherical micelles was found to coexist with the cylindrical ones, even above the percolation threshold. The shape transformation was correlated with a viscosity leap observed in the rheometry measurements. Reverse micelles at low water content under shear act as a Newtonian fluid, without any detectable shape changes. In contrast, reverse micelles at high water content behave as a shear thinning fluid. SAXS measurements at high water content under shear force have shown that the shear forces induced alignment of the cylindrical micelles in the flow direction, without any other changes in the micelle dimensions. The anisotropy parameter, a measure of the degree of the spatial order, was found to increase with increasing water content and shear rate.