Computer simulations are well established third pillar of the modem natural sciences. It complements the experiment and theory, and to the emerging the fourth pillar, the extraction of the new knowledge from the big data sets. The conference Computer simulations in Physics and beyond (CSP2020) are multidisciplinary meetings focusing on computational physics and related subjects. Indeed, computational physics methods prove useful in a broad spectrum of research in multiple natural sciences branches, and this volume provides a sample. The applications of machine learning in the natural sciences were presented at CSP2020 as well.This volume collects the refereed papers based on plenary, invited, and oral talks and the posters presented at the Fourth International Conference on Computer Simulations in Physics and beyond (CSP2020), which took place October 12-16, 2020 in Moscow. The CSP2020 conference continues the tradition started by an inaugural conference in 2015. It was jointly organized by the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics, and Science Center in Chernogolovka.This year is unusual for the CSP conference due to the pandemic. We understood the difficulty for some participants to come to Moscow, taking into account the lockdowns around the world. Consequently, we change the usual format of the Conference: both plenary talks and parallel sessions will be afternoon due to the equilibration of the time zone differences around the globe. Parallel sessions include the contributed talks (20 min) and the poster talks (short online talks up to 10 min). We decided to add an epilogue to discuss the experience of shifting the conference online during a pandemic. The discussion particularly emphasizes the advantages and disadvantages of that move. We wrote the epilogue with the hope that our modest experience can be useful to other conference organizers.We hope that this volume will interest readers, and we are already looking forward to the next conference in the series.Moscow, RussiaDecember, 2020CSP2020 Conference Chair and Volume EditorLev Shchurhttp://csp2020.ac.ru/