After 87 years, Stewart's fundamental conceptual contribution, the indicator-dilution method for measuring blood flow, is still the basis for a variety of common, practical, and minimally invasive clinical techniques. Given the spectrum of available indicators and their corresponding sensing techniques, we review the relevant transport theory and required assumptions. Various previous developments in the theory of flow and volume measurement are brought together in a formal restatement, based on the general case of dilution of volume indicators, rather than just the special case of mass indicators. The importance of each of the required assumptions is evaluated. Examples discussed include the use of conductivity modifiers and thermal indicators, with and without pulsatile flow. The formalism developed is intended to be helpful in assessing the opportunities and limitations associated with any proposed new indicator-dilution application.