During development, for tissue maintenance, and in diseases, as cells proliferate, they transition between functionally and molecularly distinct states. Dysregulation of transitions between cell states can lead to pathologies such as cancer. In many biological systems, we would like to know which transitions can occur, in what sequence, and at what rates. Current single-cell methods have expanded our ability to identify distinct cell states but not our ability to directly measure their dynamics. For example, state of the art single-cell techniques can measure the expression levels of thousands of genes, but they destroy the cells in the process, and provide only static snapshots. In our lab, we combine experiments and theory to understand the complex dynamics of cell state transitions in development and in disease. To do so, we expand and combine emerging experimental techniques. For example, we use time-lapse microscopy to track the lineage history of individual cells as they divide, followed by single-molecule imaging to readout the expression levels of multiple genes in the same cells. We also use synthetic biology to engineer novel genetic circuits that can record histories of cell lineages and major transitions in each cell's own genome. In particular, we use these approaches to uncover the dynamics of differentiation and proliferation of cancer cells in individual patients with a certain types of blood cancer called myeloproliferative neoplasm. In this cancer, intriguingly, the same genetic alteration can result in different disease phenotypes in different patients. We are trying to resolve this disconnect between genotype and phenotype.