EuPRAXIA is a distributed, compact and innovative accelerator facility based on plasma technology. In its first phase, its consortium of 51 institutes and industry partners will construct an electron-beam-driven plasma accelerator in the metropolitan area of Rome. In its second phase, EuPRAXIA will build one laser-driven plasma accelerator at a site to be chosen between several options in Europe. EuPRAXIA will serve users in ultra-fast science, e.g. on high-resolution medical imaging, deeply penetrating positron annihilation spectroscopy for materials and with Europe’s most southern free-electron laser (FEL). It will offer fascinating capabilities for research on biomolecules, viruses and microscopic processes. EuPRAXIA will thus be a transformative step in the development of ultra-compact accelerators and applications. The EuPRAXIA RI will demonstrate an innovative electron accelerator based on plasma wakefield acceleration, with a beam energy of 1 to 5 GeV and a beam quality equivalent to present radiofrequency (RF) linear accelerators, and demonstrated benefits in size and cost. EuPRAXIA will implement this strategic vision by streamlining and integrating the efforts of accelerator, plasma and laser research communities, in association with European industry, to bring plasma accelerators to the users and the market. A key short-term impact of EuPRAXIA lies in the collaboration of its 51 organisations, institutes and industry partners. It proposes a model for the construction of plasma accelerators in a fair and distributed open innovation approach beneficial to consortium partners, industry, and researchers. Major technical innovation will be furthered in plasma accelerating stages, RF technology, ultra-fast synchronisation and electronics, the development of compact, high-field quality accelerator magnets, high-repetition-rate, petawatt-scale laser systems, as well as in fast detector technology for photon science and high-energy physics. Europe’s position in plasma accelerators, high-power lasers and compact applications will be further strengthened in the context of an intense international competition. In the medium term, the EuPRAXIA energy range and performance goals will enable versatile applications in various domains, including a compact FEL, compact sources for medical imaging and positrons, tabletop test beams for particle detectors, and highly mobile but deeply penetrating X-ray and gamma-ray sources for material testing. EuPRAXIA will increase the overall capacity for user experiments in photon and accelerator science in Europe, and will provide beam characteristics not available elsewhere, such as ultra-short radiation bursts, almost point-like emissions of X-rays with benefits in resolution and higher-energy positrons from an ultra-compact source. In the long term, the progress towards ultra-compact and more cost-effective accelerators and applications, which is in EuPRAXIA’s core mission, will lower the entry barrier for accelerator-assisted research, allowing access to research groups and countries typically not making use of particle accelerators. In the long term, we envisage that a new generation of fully industrialized, highly compact particle accelerators is developed for wide usage in research centres, universities, hospitals and companies, complementing large-scale RF accelerator facilities.