Weak lensing of the cosmic microwave background is a source of cosmological information from the redshift range z=3-5 which is difficult to probe by other means. The statistical detection of the statistical homogeneity-breaking by Planck in excess of 40 sigma has allowed the determination of cosmological parameters on the percent-level. In the interpretation of the signal one usually assumes Gaussian statistics of the deflecting large-scale structure, which is only approximately true due to non-Gaussianity generation in nonlinear structure formation. I show a few results that we obtained in relaxing the assumption on Gaussianity, both using analytical and numerical methods, and conceptual results concerning the CMB-lensing formalism.