Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level. Phenotypes can be robust either against heritable perturbations (e.g., mutations) or nonheritable perturbations (e.g., the weather). Here we primarily focus on the first kind of robustness--genetic robustness--and survey three growing avenues of research: (1) measuring genetic robustness in nature and in the laboratory; (2) understanding the evolution of genetic robustness: and (3) exploring the implications of genetic robustness for future evolution.