I review the role of renormalization theory in many-fermion systems, both from the point of view of mathematical physics and that of applications to models of correlated electrons in solids. The Wilsonian renormalization group method allows for an unbiased analysis of competing ordering tendencies, such as magnetism and superconductivity in effectively two-dimensional systems. As an example, I will consider ferromagnetism and superconductivity in the Hubbard model at Van Hove filling.