This paper gives an account of three projects funded by the European Union that heavily rely on numerical modeling and simulations of nuclear reactors: the CORTEX project (CORe monitoring Techniques and EXperimental validation and demonstration), the McSAFER project (High-Performance Advanced Methods and Experimental Investigations for the Safety Evaluation of Generic Small Modular Reactors), and the METIS project (MEthods and Tools Innovations for Seismic risk assessment). The CORTEX project focuses on neutronic simulations, the McSAFER project considers neutronic, thermal-hydraulic, and thermo-mechanic simulations, whereas the METIS project investigates simulations for seismic assessments. Although the projects have different objectives, they present some common features in terms of the complementary modeling approaches used in each project and in terms of verification and validation programs. The main achievements of the projects are presented in the paper covering the technical aspects of the respective projects, training, education, and dissemination activities, as well as utilization and cross-fertilization. All three projects lead to the advancement in nuclear reactor modeling in the above areas, with the development of new simulation capabilities beyond the state-of-the-art.