The inherent stochasticity in the gene product levels can drive single cells within an isoclonal population to different phenotypic states. The dynamic nature of this intercellular variation, where individual cells can transition between different states over time, makes it a particularly hard phenomenon to characterize. We reviewed recent progress in leveraging the classical Luria–Delbrück experiment to infer the transient heritability of the cellular states. Similar to the original experiment, individual cells were first grown into cell colonies, and then, the fraction of cells residing in different states was assayed for each colony. We discuss modeling approaches for capturing dynamic state transitions in a growing cell population and highlight formulas that identify the kinetics of state switching from the extent of colony-to-colony fluctuations. The utility of this method in identifying multi-generational memory of the both expression and phenotypic states is illustrated across diverse biological systems from cancer drug resistance, reactivation of human viruses, and cellular immune responses. In summary, this fluctuation-based methodology provides a powerful approach for elucidating cell-state transitions from a single time point measurement, which is particularly relevant in situations where measurements lead to cell death (as in single-cell RNA-seq or drug treatment) or cause an irreversible change in cell physiology.