Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreements No 826078 (R.R., J.M., N.K.W., J.B.) and No 777111 (T.K., J.B.). M.Z. received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant no. K.V.S. acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant TranSYS (grant no. This publication reflects only the authors' view, and the European Commission is not responsible for any use that may be made of the information it contains. J.B., T.K., M.L. and Z.L. were supported by the German Federal Ministry of Education and Research (BMBF) within the e:Med framework (J.B., T.K., M.L. and Z.L.: grant no.

Market pull for better factory automation and the ever-increasing relevance of software in every domain are triggering a rethink in how we develop software for robotics. Techniques such as Model Driven Engineering (MDE), proven effective in businesses like automotive and aerospace, can be used to this end. Practices such as collaborative development through Open-Source Software (OSS) can also be used. Two projects funded by the European Horizon 2020 research and innovation programme are exploring these opportunities, in a common foundational effort for an EU Digital Industrial Platform for Robotics. RobMoSys, coordinated by the French Alternative Energies and Atomic Energy Commission, envisions a composition-oriented approach to system-of-system integration which is independent of the current code-centric robotic platforms, yet can build on top of them.