In this talk, I will first introduce the motivation of numerical analysis of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients. Then, I will present some recent works on strong and weak convergences of full-discretization for such SPDEs, including stochastic Allen-Cahn equation, stochastic Cahn-Hilliard equation and stochastic wave equation with nonlinear damping. Finally, future work will be given.