X chromosome inactivation (XCI) silences transcription from one of the two X chromosomes in female mammalian cells to balance expression dosage between XX females and XY males. XCI is, however, incomplete in humans: up to one-third of X-chromosomal genes are expressed from both the active and inactive X chromosomes (Xa and Xi, respectively) in female cells, with the degree of 'escape' from inactivation varying between genes and individuals. The extent to which XCI is shared between cells and tissues remains poorly characterized, as does the degree to which incomplete XCI manifests as detectable sex differences in gene expression and phenotypic traits. Here we describe a systematic survey of XCI, integrating over 5,500 transcriptomes from 449 individuals spanning 29 tissues from GTEx (v6p release) and 940 single-cell transcriptomes, combined with genomic sequence data. We show that XCI at 683 X-chromosomal genes is generally uniform across human tissues, but identify examples of heterogeneity between tissues, individuals and cells. We show that incomplete XCI affects at least 23% of X-chromosomal genes, identify seven genes that escape XCI with support from multiple lines of evidence and demonstrate that escape from XCI results in sex biases in gene expression, establishing incomplete XCI as a mechanism that is likely to introduce phenotypic diversity. Overall, this updated catalogue of XCI across human tissues helps to increase our understanding of the extent and impact of the incompleteness in the maintenance of XCI.