This paper is a written summary of an overview oral presentation given at the 1st Spanish Fusion High Performance Computer (HPC) Workshop that took place on the 27 November 2020 as an online event. Given that over the next few years ITER24 will move to its operation phase and the European-DEMO design will be significantly advanced, the EUROfusion consortium has initiated a coordination effort in theory and advanced simulation to address some of the challenges of the fusion research in Horizon EUROPE (2021–2027), i.e. the next EU Framework Programme for Research and Technological Development. This initiative has been called E-TASC, which stands for EUROfusion-Theory and Advanced Simulation Coordination. The general and guiding principles of E-TASC are summarized in this paper. In addition, an overview of the scientific results obtained in the pilot phase (2019–2020) of E-TASC are provided while highlighting the importance of the required progress in computational methods and HPC techniques. In the initial phase, five pilot theory and simulation tasks were initiated: towards a validated predictive capability of the low to high transition and pedestal physics; runaway electrons in tokamak disruptions in the presence of massive material injection; fast code for the calculation of neoclassical toroidal viscosity in stellarators and tokamaks; development of a neutral gas kinetics modular code; European edge and boundary code for reactor-relevant devices. In this paper, we report on recent progress made by each of these projects.