Our incomplete understanding of the relationship between genotypes and phenotypes makes it extremely difficult to understand and predict the evolution of diverse phenotypes in nature. Phenotypes evolve on the basis of genetic alterations. Gene regulatory networks (GRNs) build the link between genotypes and phenotypes. Using well-characterized GRNs as models may get us closer to understand the relationship between genotypes and phenotypes. Taking advantage of powerful yeast genetics, this dissertation uses the yeast GALactose (GAL) utilization networks as a model and carefully dissects three levels of evolutionary mechanisms between genotypes and phenotypes. The three levels include the functional divergence of individual genes, divergence of GRN activities, and the co-evolution between individual genes and between interacting GRNs. Through these three levels of characterization, I reveal that GAL network activity is constrained by downstream glycolysis capacity. This is likely a general constraint to sugar metabolized through glycolysis. I further examine recurring genetic changes underlying repeated tuning of GAL network activities across multiple genera and reveal a general pleiotropic constraint at the bottleneck of galactose metabolism. These constraints even enable remarkable prediction of GAL network activities merely based on DNA sequences. Understanding the genetic and functional basis of trait divergence reveals general evolutionary constraints and allows us to predict evolutionary outcomes.