Molecular regulation of cell fate decisions underlies health and disease. In my talk, I will present mathematical and statistical models that describe molecular interactions, differentiation decisions, and single cell gene expression. We use these models to infer molecular and cellular properties from biological and biomedical data. For example, in lineage trees of differentiating blood stem cells, we often observe correlated state changes between related cells. Using these correlations and a stochastic model of the differentiation process, we find differentiation events to happen much earlier than previously anticipated. To predict differentiation prospectively, we use a deep neural network trained on image patches from brightfield microscopy and cellular movement. Surprisingly, we can detect lineage choice in blood stem cells up to three generations before conventional molecular lineage markers are observable. Finally, I will present a method for fitting stochastic models to lineage trees. Using a Bayesian inference method, we compare possible models of autoregulation, an important gene regulatory motif in stem cells.>