In this talk I will give a survey on some nonlinear methods in discrete geometry. This includes the following parts: 1. Maximum principle; 2. Continuity method; 3. Topological degree method; 4. Intersection number theory. Applying these methods, we shall obtain many interesting results, such as Birkhoff’s billiard theorem, Cyclic polygon theorem, Circle packing theorem, Midscribability theorem and so on. If time permits, I will also introduce the flow method to find these solutions.