There have been many recent analytic developments in CFTs by considering different limits of the four-point function, several already reviewed in previous journal clubs. I'll try to give a general overview of the different regimes considered, and review results, such that we can collectively discuss the results and limitations. In particular I'll review which regimes play a role in the analyticity in spin of CFT data [Caron-Huot, see also recent paper] and in the physics behind the proof of the average null energy condition using causality [1610.05308].