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This paper presents theory for compartmental models used in positron emission tomography. Both plasma input models and reference tissue input models are considered. General theory is derived and the systems are characterised in terms of their impulse response functions. The theory shows that the macro parameters of the system may be determined simply from the coefficients of the impulse response functions. These results are discussed in the context of radioligand binding studies. It is shown that binding potential is simply related to the integral of the impulse response functions for all plasma and reference tissue input models currently used in positron emission tomography. The paper also introduces a general compartmental description for the behaviour of the tracer in blood, which then allows for the blood volume induced bias in reference tissue input models to be assessed