Abstract: The problems about the nonplanar travelling fronts of reaction-diffusion equations in \mathbb R^N are proposed by some French researchers who have obtained many important results in recent ten years. Some main results about these issues are reviewed in this paper. Firstly, as an example of nonplanar travelling fronts, the model of Bunsen flames is introduced. The PDE model of this problem with two important nonlinear sources, that is, ignition temperature source and bistable source which have obvious reality background is given accordingly. Then, some qualitative properties of these nonplanar travelling fronts, including the existence, the uniqueness, the monotonicity, the stability and the properties of the level sets of the solutions are reviewed. Next, the results about the equation with KPP type source, including the existence of an infinite-dimensional manifold of nonplanar fronts, the monotonicity, the stability and the properties of minimal propagation speed are introduced. At last, some other relative results in this field are reviewed and then some open questions in this subject are proposed.