We present the LUXE experiment which plans on using the European XFEL electron beam in Hamburg, Germany, with an energy of 14 − 17.5 GeV and a high intensity optical laser to study non-perturbative QED phenomena. Perturbation theory in QED is expected to break down when the critical field value of 1.3x1018 V/m is reached. To date this has not been achieved experimentally. Such high field values are important for various astrophysical phenomena such as magnetars, inflation and black holes as well as for high energy e+e- colliders. The main focus of the experiment will be tomake measurement of the rate of laser assisted electron- positron pair production in collisions of high energy photons with an intense laser beam (the non-linear Breit-Wheeler process), and non-linear Compton scattering in electron-laser interaction. It is envisaged to use a strongly focussed optical laser with an intensity of up to 1021 W/cm2, so that values of ξ <10 will be reached and then critical field will be exceeded by about a factor of two. Thus the transition from the perturbative to the non-perturbative regime of QED can be studied. The design of the experimental setup, detector systems requirements and simulation results will be presented and discussed.