Language dynamics is a rapidly growing field that focuses on all processes related to the evolution, emergence, change, competition and extinction of languages. One of the major outcomes from this field of research is that language can be viewed as a complex adaptive dynamical system that evolves through the process of self-organization and self-regulation. According to this viewpoint, a community of language users can be seen as a dynamical system that collectively solves the problem of developing a shared communication framework through the back-and-forth signaling between the participating individuals. CSL Paris has been pioneering the activities in this area, with a special focus on how a population develops a shared set of names (Naming Game), categories (Category Game), or rules (Rule Dynamics) from scratch. The basic framework is grounded in theories of Language Games, but frequently borrows concepts and methods from the areas of statistical physics and complex systems science. These areas have proven to be extremely powerful in providing various quantitative insights into language emergence and evolution.