Using the example of $N$-jettiness at hadron colliders, I will show how we systematically deal with the breakdown of color coherence and collinear factorization. These coherence-violating effects are induced by Glauber gluons, which give rise to several new momentum modes. Their interplay also generates coherence-violating logarithms (CVLs). I will derive the anomalous dimensions required for the resummation of CVLs and demonstrate that these findings imply that most existing factorization formulas for global LHC observables must be revised accordingly. Time permitting, I will also discuss how the factorization-breaking elements of splitting functions arise naturally from a generalized Wilson-line prescription and genuine Glauber contributions.