The advent of hard X-ray free-electron lasers (XFELs), LCLS in 2009, SACLA in 2011 and the European XFEL in 2017, may prove to be the most profound development since the invention of the laser and, equally, the synchrotron. Sharp improvements in a number of laser parameters, most notably intensity and pulse duration, support this expectation. Indeed, the unprecedented opportunities and expectations have triggered considerable research activities worldwide. In my talk, I will give an overview of the experimental application of the European XFEL to explore relativistic laser plasma interactions, warm dense matter, materials in extreme conditions, and laboratory astrophysics. I will then focus on studies on high-pressure science. Since May 2019, the High Energy Density (HED) scientific instrument, together with the HIBEF user consortium at the European X-ray Free-Electron Laser Facility in Schenefeld, Germany, allows international users to investigate a wide range of materials and systems at extreme conditions [1]. European XFEL and the HIBEF user consortium [2] form a joint group of more than 40 people for HED research, development and user operation. To drive a sample from ambient conditions to extreme excitations, a variety of high energy drivers are available. In particular, we have three separate optical laser systems for warm- to hot-dense-matter creation, dynamic compression and laser-plasma interaction in electron-relativistic regime. The unique HED instrument allows to study these systems with precise ultrafast x-ray probes including spectroscopy, x-ray diffraction, small- and wide-angle scattering as well as phase contrast imaging methods. It is fully tunable in the photon energy range from 5 to 25 keV at different bandwidths, can be focused to a variety of diameters. The talk will cover in more detail work in diamond anvil cells [3] and laser-driven shock compression [4], introducing the experimental capabilities and first highlight results [5]. [1] U. Zastrau, et al., J. Synchrotron Rad. (2021). 28, 1393-1416 [2] www.hibef.de [3] Liermann et al., J. Synchrotron Rad. (2021). 28, 688-706 [4] Zastrau & McMahon, Conceptual Design Report: Dynamic Laser Compression Experiments at the HED Instrument of European XFEL, public report (2017) [5] Gorman et al., structure of high pressure Sn melt, J. Appl. Physics (2024) [6] Husband et al., Superionic water ices, (2024) Nature Comm. 15, 8256 (2024)