Some models of competition between languages introduced in the last years, inspired by population dynamics models, are reviewed. A generalized model obtained combining a simple model of language competition and a human dispersal model is introduced. This model is used to study competition of cultural traits diffusing in the same geographical area. It is found that the final configuration of the system (e.g. which and how many cultural traits survive) can be strongly affected by spatial inhomogeneities, boundary and initial conditions. Some idealized examples of boundaries are discussed; e.g., boundaries influencing directly the culture transmission, or geographical barriers, which only modulated human dispersal but not culture transmission; also in this case they can strongly affect the final distribution of the cultural traits. The effect of population growth is discussed, as well as the use of different underlying cultural diffusion models.