The paper reviews the mathematical models proposed for describing the proliferation of gliomas, the most common brain tumors, with strong dynamic invasiveness and proliferative growth. When the diffuse spreading through the brain and the heterogeneity of the tissue are considered, the growth of the tumor can be described by a reaction-diffusion equation, with the unknown quantity representing the concentration of the tumor cells. The long term expansion of the tumor can be simulated as a traveling wave, solution of the considered reaction-diffusion equation. An interesting connection between these waves and the bifurcation theory can be established

Keywords: glioma, mathematical models, traveling waves, theory of bifurcation.