Jet cross sections at high-energy colliders exhibit intricate patterns of logarithmically enhanced higher-order corrections. In particular, so-called non-global logarithms emerge from soft radiation emitted off energetic partons inside jets. While this is a single-logarithmic effect at lepton colliders, at hadron colliders phase factors in the amplitudes lead to double-logarithmic corrections starting at four-loop order. In my talk I’ll first explain the resummation of non-global logarithms at lepton colliders, where techniques for the resummation of sub-leading logarithms are now becoming available. I’ll then explain the origin of the ``super-leading’’ double logarithms at hadron colliders and discuss their resummation, which was recently achieved for the first time.