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Resummation techniques are essential for high-precision phenomenology atcurrent and future high-energy collider experiments. Perturbative computationsof cross sections often suffer from large logarithmic corrections, which mustbe resummed to all orders to restore the reliability of predictions from firstprinciples. The precise understanding of the all-order structure of fieldtheories allows for fundamental tests of the Standard Model and new physicssearches. In this white paper, we review recent progress in modern resummationtechniques and outline future directions. In particular, we focus on theresummation beyond leading power, the joint resummation of different classes oflogarithms relevant for jets and their substructure, small-$x$ resummation inthe high-energy regime and the QCD fragmentation process in the small-$z_h$limit.

Snowmass 2021 White Paper: Resummation for future colliders