Convergence between big data, high-performance computing, and the cloud is the key driving factor for sustainable economic growth in the future. Technological advances in many fields are determined by competence to gain precise information from the large amounts of data collected, which in turn requires powerful computing resources. This chapter provides an overview on the evolution of the three fields and four different points of view on their convergence provided by the CYBELE, DeepHealth, Evolve, and LEXIS projects funded by the European Union under the Horizon 2020 Programme.