On travelling water waves with general vorticity

We consider the classical problem of constructing two-dimensional travelling periodic gravity waves on water of finite depth. In the last two decades much progress has been made for waves with nonzero vorticity, also in the presence of critical layers and allowing the surface to overhang. We review recent progress of the theory, in particular with regard to finding a reformulation in the most general case which is amenable to tools from nonlinear functional analysis such as global bifurcation. These notes originate in a talk held in the Séminaire Laurent Schwartz in February 2026 and are mainly based on joint work with Erik Wahlén [19].