DNA sequencing from bulk or clonal human tissues has shown that genetic mosaicism is common and contributes to both cancer and non-cancerous disorders. However, single-cell resolution is required to understand the full genetic heterogeneity that exists within a tissue and the mechanisms that lead to somatic mosaicism. Single-cell DNA-sequencing technologies have traditionally trailed behind those of single-cell transcriptomics and epigenomics, largely because most applications require whole-genome amplification before costly whole-genome sequencing. Now, recent technological and computational advances are enabling the use of single-cell DNA sequencing to tackle previously intractable problems, such as delineating the genetic landscape of tissues with complex clonal patterns, of samples where cellular material is scarce and of non-cycling, postmitotic cells. Single-cell genomes are also revealing the mutational patterns that arise from biological processes or disease states, and have made it possible to track cell lineage in human tissues. These advances in our understanding of tissue biology and our ability to identify disease mechanisms will ultimately transform how disease is diagnosed and monitored.