Our ability to characterize protein structure and dynamics is vastly outpaced by the speed of modern genetic sequencing, creating a growing divide between our knowledge of biological sequence and structure. Structural modeling algorithms offer the hope to bridge this gap through computational exploration of the sequence determinants of structure diversity. In this thesis, we introduce new algorithms that enable the efficient modeling of protein structure ensembles and their sequence variants. These statistical mechanics-based constructions enable the identification of all energetically likely sequence/structure states for a family of proteins. Beyond improved structure predictions, this approach enables a framework for thermodynamically-driven mutational and comparative analysis as well as the approximation of kinetic protein folding pathways. We have applied these techniques to two protein types that are notoriously difficult to characterize biochemically: transmembrane P-barrel proteins and amyloid fibrils. For these we advance the state-of-the-art in structure prediction, mutational analysis, and sequence alignment. Further, we have collaborated to apply these methods to open scientific questions about amyloid fibrils and bacterial biofilms.