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The process of evolution under domestication has been studied using phylogenetics, population genetics-genomics, quantitative trait locus (QTL) mapping, gene expression assays, and archaeology. Here, we apply an evolutionary quantitative genetic approach to understand the constraints imposed by the genetic architecture of trait variation in teosinte, the wild ancestor of maize, and the consequences of domestication on genetic architecture. Using modern teosinte and maize landrace populations as proxies for the ancestor and domesticate, respectively, we estimated heritabilities, additive and dominance genetic variances, genetic-by-environment variances, genetic correlations, and genetic covariances for 18 domestication-related traits using realized genomic relationships estimated from genome-wide markers. We found a reduction in heritabilities across most traits, and the reduction is stronger in reproductive traits (size and numbers of grains and ears) than vegetative traits. We observed larger depletion in additive genetic variance than dominance genetic variance. Selection intensities during domestication were weak for all traits, with reproductive traits showing the highest values. For 17 of 18 traits, neutral divergence is rejected, suggesting they were targets of selection during domestication. Yield (total grain weight) per plant is the sole trait that selection does not appear to have improved in maize relative to teosinte. From a multivariate evolution perspective, we identified a strong, nonneutral divergence between teosinte and maize landrace genetic variance-covariance matrices (G-matrices). While the structure of G-matrix in teosinte posed considerable genetic constraint on early domestication, the maize landrace G-matrix indicates that the degree of constraint is more unfavorable for further evolution along the same trajectory.