Transversity observables, such as the T-odd Sivers single-spin asymmetry measured in deep inelastic lepton scattering on polarized protons and the distributions which are measured in deeply virtual Compton scattering, provide important constraints on the fundamental quark and gluon structure of the proton. In this talk I discuss the challenge of computing these observables from first principles; i.e.; quantum chromodynamics, itself. A key step is the determination of the frame-independent light-front wavefunctions (LFWFs) of hadrons -- the QCD eigensolutions which are analogs of the Schr\"odinger wavefunctions of atomic physics. The lensing effects of initial-state and final-state interactions, acting on LFWFs with different orbital angular momentum, lead to $T$-odd transversity observables such as the Sivers, Collins, and Boer-Mulders distributions. The lensing effect also leads to leading-twist phenomena which break leading-twist factorization such as the breakdown of the Lam-Tung relation in Drell-Yan reactions. A similar rescattering mechanism also leads to diffractive deep inelastic scattering, as well as nuclear shadowing and non-universal antishadowing. It is thus important to distinguish ``static" structure functions, the probability distributions computed the target hadron's light-front wavefunctions, versus ``dynamical" structure functions which include the effects of initial- and final-state rescattering. I also discuss related effects such as the J Show Partial Abstract