I will discuss recent work which shows global well-posedness of the dynamical sine-Gordon model up to the third threshold, i.e. 6π. The key novelty in the approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and which completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects. Joint with Bjoern Bringmann.