The primary objective of the ERC project is to carry out state-of-the-art cosmological hydrodynamical simulations in the context of the standard model of cosmology and beyond and to perform self-consistent comparisons with the full range of large-scale structure (LSS) cosmology tests, assessing the evidence for physics beyond the standard model. The project consisted of 10 work packages. The first half of the programme was focused on the development of cosmological hydrodynamical simulations primarily in the context of the standard model of cosmology. The second half of the project extended our simulations beyond the standard model, including massive neutrino cosmologies, dynamical dark energy cosmologies, and alternative inflationary models. We characterised the impact of processes associated with galaxy and black hole formation (and their uncertainties) on various large-scale structure observables (such as galaxy clustering, cosmic shear, galaxy cluster counts, etc.) and assessed whether claimed tensions between constraints on certain cosmological parameters from large-scale structure observations and those of the cosmic microwave background are significant (i.e. cannot be explained by said galaxy formation processes). To date, our group has published 69 publications in top international, peer-reviewed journals that deliver on the project goals. We have made our scientific results, as well as the underlying data and simulation codes, publicly available where possible. And we have given numerous presentations, both at scientific conferences and events for the general public, on our findings.