C*-algebras are algebras of bounded linear operators on Hilbert spaces. Originally introduced as a mathematical foundation for quantum physics, these structures turn out to be interesting on their own right and exhibit a rich interplay with several other mathematical disciplines. Indeed, as I will explain, several key ideas which were initially developed to classify C*-algebras also lead to classification results for topological dynamical systems. At the same time, it was discovered recently that all C*-algebras which have been classified arise from dynamics in a precise sense. Surprisingly, this circle of ideas also leads to new constructions of groups which answered several open questions in group theory.