Changing a single nucleotide in a genome can have profound consequences under some conditions, but the same change can have no consequences under others. Indeed, organisms can be surprisingly robust to environmental and genetic perturbations. Yet, the mechanisms underlying such robustness are controversial. Moreover, how they might affect evolutionary change remains enigmatic. Here, we review the recently appreciated central role of protein homeostasis in buffering and potentiating genetic variation and discuss how these processes mediate the critical influence of the environment on the relationship between genotype and phenotype. Deciphering how robustness emerges from biological organization and the mechanisms by which it is overcome in changing environments will lead to a more complete understanding of both fundamental evolutionary processes and diverse human diseases.