In this talk, I will present the bifurcations and complex dynamics in some commonly used predator-prey systems with a nilpotent singular point. The complex dynamics are usually associated with bifurcations including saddle-node bifurcation, Hopf bifurcations, Bogdanov Takens bifurcation, in some cases bifurcations of nilpotent singularities of elliptic or focus type. I will explain and show the existence of two or three limit cycles and discuss the number of relaxation oscillations of some predator prey systems. In the end, I will introduce some latest results on the number of limit cycles of quadratic systems.