As in all biological systems, neurons and their networks must balance precision with variability. Phenotypic precision and phenotypic variability can both occur with remarkable robustness, where robustness is defined as the ability to tolerate perturbation. Variability in genotype-phenotype mapping produces phenotypic variability despite identical genetic information. The resulting variability among genetically identical neurons can contribute to the robustness of brain development. Similarly, variability of genetically identical individuals can contribute to evolutionary robustness. We discuss here shared principles of developmental robustness and evolutionary robustness, and highlight scenarios where such principles result in neural networks that achieve robustness of precision or variability.