© 2020 Annual Reviews Inc.. All rights reserved. Protein folding in the cell is mediated by an extensive network of >1,000 chaperones, quality control factors, and trafficking mechanisms collectively termed the proteostasis network. While the components and organization of this network are generally well established, our understanding of how protein-folding problems are identified, how the network components integrate to successfully address challenges, and what types of biophysical issues each proteostasis network component is capable of addressing remains immature. We describe a chemical biology-informed framework for studying cellular proteostasis that relies on selection of interesting protein-folding problems and precise researcher control of proteostasis network composition and activities. By combining these methods with multifaceted strategies to monitor protein folding, degradation, trafficking, and aggregation in cells, researchers continue to rapidly generate new insights into cellular proteostasis.