We shall discuss in this talk some aspects of the vortex motion for different nonlinear transport models arising in fluid dynamics such as Euler equations and the inviscid generalized surface quasi-geostrophic equations. The main concern is to establish the existence of rotating vortex patches (also called V-states) for different topological structures: simply connected and doubly connected patches. The proofs are based on the bifurcation theory combined with special functions.The existence of the V-states in a disc and their interaction with the boundary will also be analyzed. The content of this lecture is based on joint papers with de-La Hoz, Hmidi and Mateu.