Gene expression is regulated both by cis elements, which are DNA segments closely linked to the genes they regulate, and by trans factors, which are usually proteins capable of diffusing to unlinked genes. Understanding the patterns and sources of regulatory variation is crucial for understanding phenotypic and genome evolution. Here, we measure genome-wide allele-specific expression by deep sequencing to investigate the patterns of cis and trans expression variation between two strains of Saccharomyces cerevisiae. We propose a statistical modeling framework based on the binomial distribution that simultaneously addresses normalization of read counts derived from different parents and estimating the cis and trans expression variation parameters. We find that expression polymorphism in yeast is common for both cis and trans, though trans variation is more common. Constraint in expression evolution is correlated with other hallmarks of constraint, including gene essentiality, number of protein interaction partners, and constraint in amino acid substitution, indicating that both cis and trans polymorphism are clearly under purifying selection, though trans variation appears to be more sensitive to selective constraint. Comparing interspecific expression divergence between S. cerevisiae and S. paradoxus to our intraspecific variation suggests a significant departure from a neutral model of molecular evolution. A further examination of correlation between polymorphism and divergence within each category suggests that cis divergence is more frequently mediated by positive Darwinian selection than is trans divergence.