The Steklov problem models the vibrations of a free membrane that has all its mass concentrated along the boundary. The eigenvalues encode certain information about the geometry and topology of the membrane, but not everything! We?ll explore this idea in the two-dimensional setting, allowing the boundaries of our surfaces to have mild singularities. Some simple computations will lead to surprising results. We will also discuss bounds on the eigenvalues in terms of geometric and topological data. We will see how the orbifold setting leads naturally to considering the "sloshing" problem that describes, for instance, the free oscillations of wine in a glass. This is based on joint work with Teresa Arias-Marco, Carolyn S. Gordon, Asma Hassannezhad, Allie Ray, and Elizabeth Stanhope.