Artificial Intelligence methods and techniques have reached a high level of sophistication so that we can tackle difficult outstanding problems in science. In this talk, I will show how the question of the origins of language can be approached this way. This question has puzzled evolutionary biologists since Darwin and is still considered to be unsolved. I will outline a theory of language evolution by linguistic selection and then report a number of concrete experiments with humanoid robots that attempt to work out and validate this theory. The experiments all center around the notion of a language game, which is a routinized situated interaction that involves some form of language. Robots use linguistic strategies to evolve a communication system to deal with a particular class of language games. I will discuss examples of this and also address the question how new strategies can arise and how the robots can autonomously decide which strategies they will collectively use to bootstrap their language.