Average commercial maize yield in the US has increased from about 1Mg/ha in the 1930s to about 7Mg/ha in the 1990s. Although the increase has been the result of both genetic and agronomic-management improvements, we contend that most of this improvement is the result of the genotype×management interaction. The genetic improvement in maize yield is associated neither with yield potential per se, nor with heterosis per se, but it is associated with increased stress tolerance, which is consistent with the improvement in the genotype×management interaction. The potential for future yield improvement through increased stress tolerance of maize in the US is large, as yield potential is approximately three times greater than current commercial maize yields. The mechanism by which maize breeders have improved stress tolerance is not known, but we speculate that increased stress tolerance may have resulted from the selection for yield stability. Stability analyses were performed on a number of high-yielding maize hybrids, including three hybrids that have been involved in some of the highest maize yields recorded in producers’ fields, to examine the relationship between yield and yield stability. Results of the stability analyses showed that high-yielding maize hybrids can differ in yield stability, but results do not support the contention that yield stability and high grain yield are mutually exclusive.