The problem of Riemann Ellipsoids has an long and important history, going back to Newton, MacLaurin, Dirichlet, Riemann and Poincaré. It has its origins in the attempt to provide an explanation to the rotating figure of the Earth. In this talk, we will review this problem from the point of view of Differential Geometry and discuss how the geometric perspective can give some insight into the nonlinear stability of some of its classical solutions.