Interacting individuals tend, in general, to increase their similarity. If not influenced by his or her social environment, each individual would choose a personal response to a political question, his or her own unique cultural conventions or special correspondence between objects and words. Still, it is common experience that opinions, cultural features, and languages are shared by large groups of people. We present some dynamical models recently considered by statistical physicists to describe these processes and discuss the main results of this approach. Emphasis is on qualitative aspects such as robustness, size effects, and the role of the topology of the interaction pattern. Copyright © 2012 John Wiley & Sons, Ltd.