DNA sequences on X chromosomes often have a faster rate of evolution when compared to similar loci on the autosomes, and well articulated models provide reasons why the X-linked mode of inheritance may be responsible for the faster evolution of X-linked genes. We analyzed microarray and RNA-seq data collected from females and males of six Drosophila species and found that the expression levels of X-linked genes also diverge faster than autosomal gene expression, similar to the "faster-X" effect often observed in DNA sequence evolution. Faster-X evolution of gene expression was recently described in mammals, but it was limited to the evolutionary lineages shortly following the creation of the therian X chromosome. In contrast, we detect a faster-X effect along both deep lineages and those on the tips of the Drosophila phylogeny. In Drosophila males, the dosage compensation complex (DCC) binds the X chromosome, creating a unique chromatin environment that promotes the hyper-expression of X-linked genes. We find that DCC binding, chromatin environment, and breadth of expression are all predictive of the rate of gene expression evolution. In addition, estimates of the intraspecific genetic polymorphism underlying gene expression variation suggest that X-linked expression levels are not under relaxed selective constraints. We therefore hypothesize that the faster-X evolution of gene expression is the result of the adaptive fixation of beneficial mutations at X-linked loci that change expression level in cis. This adaptive faster-X evolution of gene expression is limited to genes that are narrowly expressed in a single tissue, suggesting that relaxed pleiotropic constraints permit a faster response to selection. Finally, we present a conceptional framework to explain faster-X expression evolution, and we use this framework to examine differences in the faster-X effect between Drosophila and mammals.