Whilst supercomputers have been around since the 1960s, experts all across the world agree that they will soon reach the height of their fame. The nature of computing is changing with an increasing number of data-intensive critical applications: by 2020, 25 billion devices will be connected and will generate over two zettabytes of traffic every year. With the European Cloud Initiative, the European Commission will provide researchers, industry, SMEs and public authorities with world-class supercomputers that bring state of the art computing and data storage capacity needed to excel in data-driven science and in the digital economy. The objective is to see a supercomputer based on EU technology among the world top three by 2022. The European strategy for HPC, implemented under Horizon 2020, is split into three pillars: developing the next generation of HPC towards exascale, achieving excellence in HPC delivery and use, and providing industry and academia with access to supercomputing facilities and services through PRACE, the pan-European world-class HPC infrastructure. The European Commission has pledged EUR 700 million in a contractual Public-Private Partnership on HPC with the European HPC stakeholders gathered in the ETP4HPC Association. More than EUR 300 million has already been committed in Horizon 2020 for HPC-related activities. For example, EUR 40 million was allocated in 2015 to launch Centres of Excellence for the application of HPC in scientific or industrial domains that are most important for Europe; the call Towards Exascale High-Performance Computing recently provided researchers with almost EUR 100 million in funding to support the development of core exascale technologies. EU researchers are already taking huge steps to bridge the gap between technical capacity and industry needs through the FORTISSIMO or NUMEXAS projects for example. From software to hardware, and with particular attention being paid to energy efficiency, projects like MONT-BLANC, DEEP/DEEP-ER, FiPS, EXA2GREEN, ADEPT and the H2020-funded EeHPC are setting the stage for a world where exascale computing will be one of the key cornerstones of the European economy. The EU's HPC strategy, together with the European Cloud initiative, is part of the digitisation of the industry package, strengthening Europe's position in data-driven innovation, improving competitiveness and cohesion, and ultimately helps to create a truly Digital Single Market in Europe.