Evolutionary genetics has recently made enormous progress in understanding how genetic variation maps into phenotypic variation. However why some traits are phenotypically invariant despite apparent genetic and environmental changes has remained a major puzzle. In the 1940s, Conrad Hal Waddington coined the concept and term "canalization" to describe the robustness of phenotypes to perturbation; a similar concept was proposed by Waddington's contemporary Ivan Ivanovich Schmalhausen. This paper reviews what has been learned about canalization since Waddington. Canalization implies that a genotype's phenotype remains relatively invariant when individuals of a particular genotype are exposed to different environments (environmental canalization) or when individuals of the same single- or multilocus genotype differ in their genetic background (genetic canalization). Consequently, genetic canalization can be viewed as a particular kind of epistasis, and environmental canalization and phenotypic plasticity are two aspects of the same phenomenon. Canalization results in the accumulation of phenotypically cryptic genetic variation, which can be released after a "decanalizing" event. Thus, canalized genotypes maintain a cryptic potential for expressing particular phenotypes, which are only uncovered under particular decanalizing environmental or genetic conditions. Selection may then act on this newly released genetic variation. The accumulation of cryptic genetic variation by canalization may therefore increase evolvability at the population level by leading to phenotypic diversification under decanalizing conditions. On the other hand, under canalizing conditions, a major part of the segregating genetic variation may remain phenotypically cryptic; canalization may therefore, at least temporarily, constrain phenotypic evolution. Mechanistically, canalization can be understood in terms of transmission patterns, such as epistasis, pleiotropy, and genotype by environment interactions, and in terms of genetic redundancy, modularity, and emergent properties of gene networks and biochemical pathways. While different forms of selection can favor canalization, the requirements for its evolution are typically rather restrictive. Although there are several methods to detect canalization, there are still serious problems with unambiguously demonstrating canalization, particularly its adaptive value.