X chromosome inactivation (XCI) silences the transcription from one of the two X chromosomes in mammalian female cells to balance expression dosage between XX females and XY males. XCI is, however, characteristically 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 individuals1,2 (Fig. 1). However, the extent to which XCI is shared between cells and tissues remains poorly characterized3,4, as does the degree to which incomplete XCI manifests as detectable sex differences in gene expression5 and phenotypic traits6. Here we report a systematic survey of XCI using a combination of over 5,500 transcriptomes from 449 individuals spanning 29 tissues, and 940 single-cell transcriptomes, integrated with genomic sequence data (Fig. 1). By combining information across these data types we show that XCI at the 683 X-chromosomal genes assessed 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 new escape genes supported by multiple lines of evidence, and demonstrate that escape from XCI results in sex biases in gene expression, thus establishing incomplete XCI as a likely mechanism introducing phenotypic diversity6,7. Overall, this updated catalogue of XCI across human tissues informs our understanding of the extent and impact of the incompleteness in the maintenance of XCI.