Abstract: We consider two-dimensional steady gravity waves in finite-depth water. We prove that, for any supercritical Froude number, there exists a continuous one-parameter family of solitary waves in equilibrium with a submerged point vortex. This family bifurcates from an irrotational uniform flow, and, at least for large Froude numbers, extends up to the development of a surface singularity. These are the first rigorously constructed gravity wave-borne point vortices without surface tension. Notably our formulation allows the free surface to be overhanging, and we provide numerical evidence that strongly suggests that some of these waves indeed overturn. Finally, we prove that at generic solutions on the parameter family-including those that are large amplitude or even overhanging-the point vortex can be desingularized to obtain solitary waves with a submerged hollow vortex. Physically, these can be thought of as traveling waves carrying spinning bubbles of air.