Transverse-momentum-dependent distributions (TMDs) provide a description of hadron structure and hadronization in 3D momentum space in terms of quarks and gluons, the elementary degrees of freedom of QCD. As such, they are among the nonperturbative links between hadrons and elementary particles. At variance with the collinear one-dimensional distribution and fragmentation functions, TMDs take into account the spin-momentum correlations between the hadron and its elementary constituents and are thus more rich and informative. We know how to define the TMDs by means of operators in QCD. Nonetheless, there are many nontrivial open questions concerning the TMDs. For example, their emergence from factorization theorems in hard scattering processes, their universality properties, their functional form at low transverse momentum, and its flavor dependence. Over the past years, thanks to a fruitful synergy of theoretical and experimental investigations, we have made significant progress in the study of TMDs and hadron structure in 3D momentum space, but we are still far from a complete understanding. In this talk I will review theoretical and phenomenological aspects of TMDs, connecting the physics programs of Jefferson Lab and the LHC, and stressing the relevance of an Electron-Ion Collider for improving our quantitative understanding of hadron structure.