Weak lensing analyses have so far relied mainly on two-point statistics, which are optimal only under Gaussian assumptions. On non-linear scales, higher-order shear statistics capture additional cosmological information and respond differently to intrinsic alignments and baryonic effects, providing valuable consistency checks. In this talk, I will review recent progress on modeling and measuring third-order cosmic shear, including advances in emulator-based bispectrum predictions, treatments of intrinsic alignments and baryonic effects, and fast estimators for three-point functions. I will highlight current constraints from KiDS, DES, and HSC.
Looking forward, I will argue that third-order statistics provide a natural application for simulation-based inference (SBI): their likelihoods are non-Gaussian, covariance and systematics modeling already rely on simulations, and SBI allows us to incorporate these effects flexibly. I will outline the opportunities and challenges of combining SBI with higher-order lensing as a complementary path toward field-level inference.