The finite element approximation of the eigenvalues of Maxwell's equations has been the object of a wide investigation. It is now quite understood that the natural and efficient choice is to use Nedelec (edge) finite element spaces. On the other hand, there are various reasons why people might prefer to use standard Lagrange (nodal) finite element spaces. In this talk we review the main results related to this topic and present some recent research on the nodal finite element approximation of Maxwell's eigenproblem.