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Clonal hematopoiesis (CH) results from the acquisition and expansion of somatic mutations in hematopoietic stem and progenitor cells and is associated with age-related clinical sequelae, including an increased risk for cardiovascular disease, myeloid neoplasms and complications related to cancer therapy. Chemotherapy and radiation can accelerate CH expansion and further elevate the risk of adverse events, including cardiotoxicity and therapy-related myeloid neoplasms. Although CH is increasingly recognized as a clinically relevant precursor state and predictive biomarker, the long-term dynamics of CH expansion in humans remain poorly understood. Longitudinal data are often collected but not integrated with mathematical prediction. Mathematical modeling is essential for characterizing CH evolution, estimating clone fitness, inferring stem cell pool dynamics and enabling patient-level predictions. This study summarizes the current evidence on CH dynamics in humans, compares mathematical models used to predict CH progression, assesses the validity of model assumptions and discusses the implications for clinical management of individuals with these precursor conditions.