Various processes employing strong laser fields with intensities likely available in the near future are considered. Emphasis is put on the possibility of probing the nonlinear properties of the quantum vacuum experimentally. We investigate the diffractive effects arising in the interaction between an x-ray probe and an intense, focused optical standing wave. The enhancement of vacuum polarization effects (VPEs) in the presence of a cold plasma is shown. The study of the properties of quantum vacuum is closely related to the possibility of testing quantum electrodynamics in the presence of strong background fields. We investigate in detail how laser photons can merge due to VPEs when interacting with the electromagnetic field of a high-energy proton. We show that the laser photon merging rate manifests an observable, non-perturbative dependence on the laser field parameters.