Particle accelerators based on RF systems have been a remarkable success story since they were proposed 90 years ago by Ising and demonstrated experimentally by Wideröe. Today there are some 30,000 accelerators world-wide, from small industrial accelerators to the Large Hadron Collider, one of mankind largest machines. The maximum beam energy in particle accelerators has for many years followed an exponential increase with time, the so-called Livingston curve. However, progress has slowed down significantly over the last years. At the same time the new technology of plasma-based electron accelerators has emerged with exponential progress since 1980. Acceleration lengths are a factor 100-1000 shorter than in conventional accelerators. Plasmas excited by industrially available lasers have produced accelerating gradients of up to 100 GV/m and electrons at energies up to 4.25 GeV, promising a revolution in the way accelerators are built. Much more compact and cost-effective accelerators can be imagined. The potential of this technology is discussed. National and international activities are summarized. Special emphasis will be placed on the “European Plasma Research Accelerator with Excellence in Applications” (EuPRAXIA) project, the second accelerator-related EU design study in Horizon2020. This EU-financed study aims at proposing a European Research Infrastructure that pioneers a compact plasma accelerator for applications in photon science, High Energy Physics and other fields, like medical imaging applications. EuPRAXIA is supported by a consortium of 16 member institutes and presently 15 associated partner labs in Europe, Asia and the US.