Abstract Somatic evolution is a novel emerging frontier in human biology, as cells within diverse normal and malignant tissues have been shown to diversify and undergo selection. We and others have shown that somatic evolution is driven by both genetic and non-genetic modes of inheritance (Cell, 2013; Cancer Cell, 2014; Nature, 2015; Nature Communications 2016 & 2019; Cell Systems, 2019). A key challenge is to integrate across these different layers of information at the level of the single cell – the atomic unit of the evolutionary process (Nature Reviews Genetics, 2020). To address this challenge, we have developed single-cell multi-omics technologies and analytical frameworks to link genetic, epigenetic and phenotypic information (Nature, 2019a & Nature, 2019b). We have applied these methods to chart how somatic mutations reshape the differentiation topographies of neoplastic and normal hematopoiesis (Nature, 2019a; Nature Genetics, 2020), as well as defined the epigenetic encoding, inheritance, and plasticity of malignant transcriptional cell states (Nature, 2019b; Nature Genetics, 2021). Citation Format: Dan Landau. Charting normal and malignant differentiation topologies with single-cell multi-omics [abstract]. In: Proceedings of the AACR Special Conference on the Evolutionary Dynamics in Carcinogenesis and Response to Therapy; 2022 Mar 14-17. Philadelphia (PA): AACR; Cancer Res 2022;82(10 Suppl):Abstract nr IA008.