Massive international efforts are currently being deployed to construct predictions tools for upcoming weak lensing analyses, typically aiming at sub-percent precision. Their focuses are primarily set on two-point statistics (e.g. position and/or shape correlation functions), mainly because these can be directly related to the matter power spectrum, which can be accurately obtained from fitting functions and emulators. Weak lensing beyond the two-point statistics can play an important role, for it has access to more cosmological information given that the matter density field has become non-Gaussian. In this talk I will review recent weak lensing data analysis based on higher order statistics, and discuss requirements for upcoming surveys, with a focus on the calibration with cosmological simulations.