A fundamental question in the biology of sex differences has eluded direct study in humans: How does sex-chromosome dosage (SCD) shape genome function? To address this, we developed a systematic map of SCD effects on gene function by analyzing genome-wide expression data in humans with diverse sex-chromosome aneuploidies (XO, XXX, XXY, XYY, and XXYY). For sex chromosomes, we demonstrate a pattern of obligate dosage sensitivity among evolutionarily preserved X-Y homologs and update prevailing theoretical models for SCD compensation by detecting X-linked genes that increase expression with decreasing X- and/or Y-chromosome dosage. We further show that SCD-sensitive sex-chromosome genes regulate specific coexpression networks of SCD-sensitive autosomal genes with critical cellular functions and a demonstrable potential to mediate previously documented SCD effects on disease. These gene coexpression results converge with analysis of transcription factor binding site enrichment and measures of gene expression in murine knockout models to spotlight the dosage-sensitive X-linked transcription factor ZFX as a key mediator of SCD effects on wider genome expression. Our findings characterize the effects of SCD broadly across the genome, with potential implications for human phenotypic variation.