In this review, we trace the origins of mathematical modeling methods and pay particular attention to radiotracer applications. Nuclear medicine has been advanced greatly by the efforts of the Society of Nuclear Medicine's Medical Internal Radiation Dose Committee. Well-developed mathematical methods and tools have been created in support of a wide range of applications. Applications of mathematical modeling extend well beyond biology and medicine and are essential to analysis is a wide range of fields that rely on numerical predictions, eg, weather, economic, and various gaming applications. We start with the discovery of radioactivity and radioactive transformations and illustrate selected applications in biology, physiology, and pharmacology. We discuss compartment models as tools used to frame the context of specific problems. A definition of terms, methods, and examples of particular problems follows. We present models of different applications with varying complexity depending on the features of the particular system and function being analyzed. Commonly used analysis tools and methods are described, followed by established models which describe dosimetry along gastrointestinal and urinary excretory pathways, ending finally with a brief discussion of bone marrow dose. We conclude pointing to more recent, promising methods, not yet widely used in dosimetry applications, which aim at coupling pharmacokinetic data with other patient data to correlate patient outcome (benefits and risk) with the type, amount, kind and timing of the therapy the patient received.