  Resummation techniques are essential for high-precision phenomenology at
current and future high-energy collider experiments. Perturbative computations
of cross sections often suffer from large logarithmic corrections, which must
be resummed to all orders to restore the reliability of predictions from first
principles. The precise understanding of the all-order structure of field
theories allows for fundamental tests of the Standard Model and new physics
searches. In this white paper, we review recent progress in modern resummation
techniques and outline future directions. In particular, we focus on the
resummation beyond leading power, the joint resummation of different classes of
logarithms relevant for jets and their substructure, small-$x$ resummation in
the high-energy regime and the QCD fragmentation process in the small-$z_h$
limit.
