Many processes in biology, including organ development, tumor growth, and adaptive immunity unfold over time in a way that originates from a small progenitor population and progresses through cell division and selective expansion of sub-clones. The emerging field of single-cell lineage tracing provides a unique opportunity to study these processes at an unparalleled resolution by tracking the clonal history of individual cells, while at the same time recording their transcriptomes. Our group is harnessing Cas9- based lineage tracing technologies to study clonal processes, with the current emphasis on tumor growth and its association with immunity. To enable these studies, we are developing the accompanying algorithms and software, targeting different aspects of the work such as inference of lineage trees and its theoretical guarantees, estimation of divergence times, analysis of heritable transcriptional programs, and analysis of transcriptional changes that take place during the evolution of clonal populations. This work brings together ideas from graph algorithms, statistical phylogenetics and generative modeling powered by deep learning.