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Mutation data reveal the dynamic equilibrium between DNA damage and repair processes in cells and are indispensable to the understanding of age-related diseases, tumor evolution, and the acquisition of drug resistance. However, available genome-wide methods have a limited ability to resolve rare somatic variants and the relationships between these variants. Here, we present lineage sequencing, a new genome sequencing approach that enables somatic event reconstruction by providing quality somatic mutation call sets with resolution as high as the single-cell level in subject lineages. Lineage sequencing entails sampling single cells from a population and sequencing subclonal sample sets derived from these cells such that knowledge of relationships among the cells can be used to jointly call variants across the sample set. This approach integrates data from multiple sequence libraries to support each variant and precisely assigns mutations to lineage segments. We applied lineage sequencing to a human colon cancer cell line with a DNA polymerase epsilon (POLE) proofreading deficiency (HT115) and a human retinal epithelial cell line immortalized by constitutive telomerase expression (RPE1). Cells were cultured under continuous observation to link observed single-cell phenotypes with single-cell mutation data. The high sensitivity, specificity, and resolution of the data provide a unique opportunity for quantitative analysis of variation in mutation rate, spectrum, and correlations among variants. Our data show that mutations arrive with nonuniform probability across sublineages and that DNA lesion dynamics may cause strong correlations between certain mutations.