As collider physics is entering in earnest a new precision era, probing heavy new physics indirectly and systematically, by characterising interactions between known particles is becoming of acute interest. The corresponding effective-field-theory interpretations of the data are being refined at a steady pace by theorists, and progressively implemented by experimental collaborations. They would allow us to identify challenging patterns of new physics, hidden in small deviations correlated across several observables. In this talk, I will cover recent developments in this effective-field-theory programme, from the more phenomenological to the more formal ones.