Consider a classical 2D gravity wave (studied by Euler, Poisson, Cauchy, Airy, Stokes, Levi-Civita,..., as well as many modern mathematicians) with an arbitrary vorticity function. Let the wave travel at a constant speed over a flat bed. Using local and global bifurcation theory and topological degree, one can prove that there exist many such waves of large amplitude. I will outline the existence proof, joint with Adrian Constantin, and also exhibit some recent computations, joint with Joy Ko, of these waves using numerical continuation. The computations illustrate certain relationships between the amplitude, energy and mass flux of the waves. If the vorticity is sufficiently large, the first stagnation point of the wave occurs not at the crest (as with the much- studied irrotational flows) but on the bed directly below the crest or else in the interior of the fluid. The vorticity also affects the pressure beneath the fluid.