The traditional structure function paradigm has provided significant insights for well-folded proteins in which structures can be easily and rapidly revealed by X-ray crystallography beamlines. However, approximately one-third of the human proteome is comprised of intrinsically disordered proteins and regions (IDPs/IDRs) that do not adopt a dominant well-folded structure, and therefore remain "unseen" by traditional structural biology methods. This Perspective considers the challenges raised by the "Dark Proteome", in which determining the diverse conformational substates of IDPs in their free states, in encounter complexes of bound states, and in complexes retaining significant disorder requires an unprecedented level of integration of multiple and complementary solution-based experiments that are analyzed with state-of-the art molecular simulation, Bayesian probabilistic models, and high-throughput computation. We envision how these diverse experimental and computational tools can work together through formation of a "computational beamline" that will allow key functional features to be identified in IDP structural ensembles.