New technologies of compact accelerators, in particular plasma accelerators, and laser-based x-ray sources, are on the verge of reaching maturity in this decade, making today the perfect time to steer them towards a broader scope of applications in academia, medicine and the industry. Training the next generation of entrepreneur-minded early-stage researchers on such a disruptive technology will enable them to start successful careers with significant societal impact. This is the goal we pursue with the Marie Skłodowska Curie Action Doctoral Network EPACE (European compact accelerators, their applications, and entrepreneurship). EPACE fosters a culture of excellence, innovation and critical thinking to help the next generation explore opportunities and guide it towards significant contributions in line with the EU missions. Emphasis is put on applications in industry (muon tomography), medicine (FLASH effect with particle beams from plasma accelerators), and impactful progress (reduced energy consumption of particle accelerators). An extensive curriculum from a world-class European business school will help the students identify and transfer the most promising innovations into commercial products. Coordinated by DESY, EPACE gathers 31 industrial and academic partners in Europe, to provide 15 PhD students with great scientific expertise, a thorough awareness of EU values and a drive towards entrepreneurship.