Being less sensitive to systematic effects, the cross-correlations between Cosmic Microwave Background (CMB) data sets and large-scale structures surveys are expected to provide excellent astrophysical and cosmological constraints in the upcoming years. In order to capitalize on the advantages offered by these joint analysis techniques, an accurate physical modeling of both the observables involved is required. I will present recent numerical results on CMB lensing simulations aiming at including effects of non-linear evolution of large-scale structures beyond the Born approximation on large fraction of the sky. If time allows, I will also discuss the status of the POLARBEAR experiment and its upgrade, the Simons Array, which will provide one of the best CMB data set for cross-correlation studies in the near future.