Jet broadening is an event-shape variable that measures the transverse momenta of particles inside jets. It has been measured precisely in e+e- annihilations and is used to extract the strong coupling constant. I will present an effective field theory approach that allows to resum logarithmic corrections to the broadening distributions in the two-jet limit. Interestingly, dimensional regularization turns out to be insufficient to regularize infrared singularities in the effective theory. One therefore needs to introduce an additional regulator, which generates an anomalous source of logarithmic corrections. I will present a factorization theorem that incorporates these contributions to all orders in perturbation theory, and I will report on recent progress in extending the resummations to next-to-next-to-leading logarithmic accuracy.