The bacterial protein quality control (PQC) network comprises a set of genes that promote proteostasis (proteome homeostasis) through proper protein folding and function via chaperones, proteases, and protein translational machinery. It participates in vital cellular processes and influences organismal development and evolution. In this review, we examine the mechanistic bases for how the bacterial PQC network influences molecular evolution. We discuss the relevance of PQC components to contemporary issues in evolutionary biology including epistasis, evolvability, and the navigability of protein space. We examine other areas where proteostasis affects aspects of evolution and physiology, including host-parasite interactions. More generally, we demonstrate that the study of bacterial systems can aid in broader efforts to understand the relationship between genotype and phenotype across the biosphere.