What do the human brain, social networks, financial systems, the universe, optical systems, metabolism or a genome have in common? They are classical examples of complex systems, i.e., systems composed of a large number of simple elements in interaction and exhibiting emerging phenomena. The main objective of naXys Research Institute is the study of such complex systems, by means of the analysis of real-world data, their modelling through mathematics and numerical simulations, and their control and optimisation. Our belief is that a proper understanding of systems requires a modelling step, which allows to identify causal relationships between various parameters and to identify the mechanisms by which they operate. This abstraction must be based on empirical validation, but the mining of data alone is neither sufficient nor satisfactory. For this reason, a knowledge of the specific domain and the use of adequate tools in modelling, analysis and simulations are essential.