In this talk we survey several results on biconservative submanifolds, with particular emphasis on biconservative hypersurfaces in Euclidean spaces that are invariant under the action of SO(p+1)×SO(q+1). Using the Poincaré?Bendixson Theorem, we analyze the dynamics of their profile curves in the orbit space and establish the existence of infinitely many complete SO(p+1)×SO(q+1)-invariant biconservative hypersurfaces in Euclidean spaces.