X inactivation--the transcriptional silencing of one X chromosome copy per female somatic cell--is universal among therian mammals, yet the choice of which X to silence exhibits considerable variation among species. X inactivation strategies can range from strict paternally inherited X inactivation (PXI), which renders females haploid for all maternally inherited alleles, to unbiased random X inactivation (RXI), which equalizes expression of maternally and paternally inherited alleles in each female tissue. However, the underlying evolutionary processes that might account for this observed diversity of X inactivation strategies remain unclear. We present a theoretical population genetic analysis of X inactivation evolution and specifically consider how conditions of dominance, linkage, recombination, and sex-differential selection each influence evolutionary trajectories of X inactivation. The results indicate that a single, critical interaction between allelic dominance and sex-differential selection can select for a broad and continuous range of X inactivation strategies, including unequal rates of inactivation between maternally and paternally inherited X chromosomes. RXI is favored over complete PXI as long as alleles deleterious to female fitness are sufficiently recessive, and the criteria for RXI evolution is considerably more restrictive when fitness variation is sexually antagonistic (i.e., alleles deleterious to females are beneficial to males) relative to variation that is deleterious to both sexes. Evolutionary transitions from PXI to RXI also generally increase mean relative female fitness at the expense of decreased male fitness. These results provide a theoretical framework for predicting and interpreting the evolution of chromosome-wide expression of X-linked genes and lead to several useful predictions that could motivate future studies of allele-specific gene expression variation.