We discuss historic aspects of 'sharp weighted estimates', notably its origins in simple probability spaces with dyadic filtrations. Some cornerstone results central to harmonic analysis will be mentioned in a historic fashion. The main part of the lecture returns to the probabilistic setting and stochastic analysis in filtered spaces with continuous time, arbitrary underlying measure and possible 'jumps'. It is proved - via two important methods from 'weights', Bellman and Sparse, that 'all' subordinate pairs of martingales have a sharp A_p bound. It is remarkable that in this generality, not even the boundedness of the maximal function seems to have been known - a fact that presents no difficulty at all with today's methods. This lecture should also serve as an introduction to techniques in 'weights' for those participating in the semester-long program.