  We survey recent results concerning ground states and bound states
$u\colon\mathbb{R}^3\to\mathbb{R}^3$ to the curl-curl problem
$$\nabla\times(\nabla\times u)+V(x)u= f(x,u) \quad\hbox{ in } \mathbb{R}^3,$$
which originates from the nonlinear Maxwell equations. The energy functional
associated with this problem is strongly indefinite due to the infinite
dimensional kernel of $\nabla\times(\nabla\times \cdot)$. The growth of the
nonlinearity $f$ is superlinear and subcritical at infinity or purely critical
and we demonstrate a variational approach to the problem involving the
generalized Nehari manifold. We also present some refinements of known results.
