In this talk, I will present the complex dynamics and bifurcations of a predator-prey system with generalized Holling-type functional responses and Allee effects in prey. The maximal codimensions of the nilpotent saddle, cusp singularity, and weak focus are analyzed and the unfoldings of Bogdanov-Takens bifurcation and nilpotent saddle bifurcation are developed. The degenerate Hopf bifurcation is studied by an equivalent generalized Lienard system. The existence and codimensions of homoclinic loops and heteroclinic loops are also discussed