Weak lensing (WL) effects arise from the gravitational light deflection by large-scale structures, and thus are powerful tools to probe the nature of the dark universe. Their signals are dominantly from relatively smallscale nonlinear structures, and therefore possess significant nonGaussianity. Statistical analyses of WL effects thus need to be multi approaches beyond two-point correlation functions. In this presentation, I will present our series studies of WL peak statistics, from model building to simulation testing and to applications to observational data to derive cosmological constraints. Opportunities and challenges for high precision cosmological studies with future large surveys will also be discussed.