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Transverse spin observables in hard-scattering hadronic processes within collinear factorization

We review what is currently known about the transverse spin structure of hadrons, in particular from observables that can be analyzed within a collinear framework. These effects have been around for 40 years and represent a critical test of perturbative QCD. We look at both proton-proton and lepton-nucleon collisions for various final states. While the main focus is on transverse single-spin asymmetries, we also discuss how longitudinal-transverse double-spin asymmetries offer a complimentary, yet equally important, source of information on the quark-gluon content of hadrons. We also summarize some recent progress in solidifying the theoretical formalism behind these observables and give an outlook on future directions of research.