It is well known that mixed-integer formulations can be used tomodel important classes of nonconvex functions, such as fixed-charge functions and linear economy-of-scale cost functions. The purpose of this paper is to formulate a rigorous definition of a mixed-integer model of a given function and to study the properties of the functions that can be so modelled. An interesting byproduct of this approach is the identification of a simple class of functions that cannot be modelled by computer-representable mixed-integer formulations, even though mixed-integer models based on the use of a single arbitrary irrational constant are available for this class.