LUXE (Laser Und XFEL Experiment)  is a new experiment that aims at combining a high-intensity optical laser with the 16.5 GeV electron beam of the European XFEL to explore the uncharted terrain of Quantum Electrodynamics (QED) at the strong-field frontier. The experiment has been designed to allow high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. The physics that can be probed at and beyond the Schwinger limit will be reviewed. The foreseen detector systems and their sensitivity are presented and compared to the state of the art theoretical predictions. The high flux of high-energetic photons created in the experiment will also allow to set limits on physics beyond the Standard Model. The experiment is planed to be constructed in DESY Hamburg by 2024 with an existing 40 TW laser system to allow first scientific data to be collected and analysed, before it will be upgraded with a 350 TW system to study in detail the non-perturbative regime.