The Horizon 2020 Project EuPRAXIA ("European Plasma Research Accelerator with eXcellence In Applications") is preparing a conceptual design report of a highly compact and cost-effective European facility with multi-GeV electron beams using plasma as the acceleration medium. The accelerator facility will be based on a laser and/or a beam driven plasma acceleration approach and will be used for photon science, high-energy physics (HEP) detector tests, and other applications such as compact X-ray sources for medical imaging or material processing. EuPRAXIA started in November 2015 and will deliver the design report in October 2019. EuPRAXIA aims to be included on the ESFRI roadmap in 2020.