Pharmacokinetic (PK) modelling has had since the beginning a systemic approach to the description of chemicals absorption, distribution, metabolism and excretion in or from the body. The earliest PK models were physiological and mechanistic in the sense that they started from a mathematical description of the body as organs of given composition and properties, linked by blood flow. For a while, the lack of fast methods for solving differential equation systems led to the formulation and use of empirical and much simpler compartmental models. Interest in physiologically based (PBPK) modelling has persisted, however, in toxicology where data are sparse, and where transpositions from animals to humans are best grounded in physiology and biochemistry. Advances in Bayesian numerical analysis now allow rigorous inferences for PBPK models, including in the context of complex data structures (e.g., hierarchical or "population" models).