The field of single-cell genomics is advancing rapidly and is generating many new insights into complex biological systems, ranging from the diversity of microbial ecosystems to the genomics of human cancer. In this Review, we provide an overview of the current state of the field of single-cell genome sequencing. First, we focus on the technical challenges of making measurements that start from a single molecule of DNA, and then explore how some of these recent methodological advancements have enabled the discovery of unexpected new biology. Areas highlighted include the application of single-cell genomics to interrogate microbial dark matter and to evaluate the pathogenic roles of genetic mosaicism in multicellular organisms, with a focus on cancer. We then attempt to predict advances we expect to see in the next few years.