Computational modelling with multi-agent systems has become an important technique in studying language evolution. We present a brief introduction into this rapidly developing field, as well as our own contributions, which include an analysis of the evolutionary naming game model. In this model, communicating agents, which try to establish a common vocabulary, are equipped with an evolutionarily selected learning ability. Such a coupling of biological and linguistic ingredients results in an abrupt transition: upon a small change of the model control parameter, a poorly communicating group of agents with small learning abilities transforms into almost perfectly communicating group of agents with large learning abilities. Genetic imprinting of the learning abilities progresses through the Baldwin effect: initially linguistically unskilled agents learn a language, which creates a niche where there is an evolutionary pressure for the increase of learning ability. Under the assumption that communication intensity increases continuously with finite speed, the transition is split into several transition-like changes. It shows that the speed of cultural changes, that sets an additional characteristic time scale, might be yet another factor affecting the evolution of language. In our opinion, this model shows that linguistic and biological processes have a strong influence on each other and this influence certainly has contributed to an explosive development of our species.