Abstract: Phase transitions happen in complex systems, systems made of very many interacting entities, and correspond to a change of macroscopic state of the system when some external control parameter is tuned. The classical example are molecules of water globally changing from ice to liquid to vapour (to plasma) as temperature increases. But in the past 50 years it has been realised that phase transitions are much more «universal», in the sense that they also happen in systems that may a priori be considered far from the realm of condensed matter physics: neurosciences, biological systems, financial markets, but also in more abstract «Information processing systems»: computer science and algorithms for combinatorial optimisation, machine learning from data, or inference of large signals hidden in noise. «No way… Yes way!»