We present relativistic models of the interaction between quantum plasmas and intense electromagnetic radiation. The models are based on collective Schroedinger, Klein-Gordon and Dirac equations to describe the dynamics of the electrons, which are coupled with the Maxwell and Poisson equations for the self-consistent electromagnetic and electrostatic fields. The models are used to investigate the nonlinear propagation and self-induced transparency of electromagnetic waves in a dense quantum plasma, and parametric instabilities giving rise to the localization of waves by the modulational instability and back-scattered waves by a Raman-type instability. Applications of the collective Klein-Gordon-Maxwell model to quantum X-ray free electron lasers, where an electromagnetic wiggler interacts with a relativistic electron beam to generate tunable X-ray radiation, are also discussed.