Most PET kinetic modeling approaches have at their basis a compartmental model that has first-order, constant coefficients. The present article outlines the one-, two-, and three-compartment models used to measure cerebral blood flow, cerebral glucose metabolism, and receptor binding, respectively. The number of compartments of each model is based on specific knowledge of the physiological and/or biochemical compartments into which the tracer distributes. Additional physical and biochemical properties of the tracer distribution are considered in specifying the use of first-order rate constants. For example, in cerebral blood flow and receptor binding studies transport across the blood-brain barrier by diffusion can be modeled as a first-order process. A saturable carrier-mediated process or saturable enzyme catalyzed reaction, when tracer doses of the labeled substrate are used and the natural substrate is in steady-state, also results in first-order rate constants, as in glucose metabolism studies. The rate of ligand binding, on the other hand, depends on the concentrations of both substrate and available receptors. In order to appropriately model the reaction as pseudo first-order during a specified experimental interval, protocols are carefully designed to assure that the number of available binding sites remains approximately constant throughout the given interval. A broad array of scanning protocols is employed for kinetic analyses. These include single-scan approaches, which function like their autoradiographic counterparts in animal studies and are often called "autoradiographic" methods, which allow estimation of a single parameter. Dynamic scanning to obtain the time course of tissue activity allows simultaneous estimation of multiple parameters. Scanning may be conducted during a period of tracer uptake or after attainment of steady-state conditions. All quantitative modeling approaches share the common requirement that an arterial input function be measured or an appropriate surrogate be found. A vast array of methods is available for estimation of model parameters, both micro and macro. In the final analysis, it is the interaction among all elements of the PET study, including careful tracer selection, model specification, experimental protocol design, and sound parameter estimation methods, that determines the quantitative accuracy of the estimates of the physiological or biochemical process under study.