Functional elastomer nanocomposites have found numerous applications in diverse hi-tech areas. Transport phenomena, such as electrical conductivity, thermal conductivity and gas/liquid barrier properties, have been the major focus of functional elastomer nanocomposite research. Despite essential progress in these areas, a summary and discussion of state-of-the-art strategies for regulating the transport performances of nanocomposites based on the transportation mechanisms of electrons, phonons and mass are lacking. In the present review, a brief introduction of transport mechanisms in elastomer nanocomposites precedes a systematic summary of the important progress in elastomer nanocomposites with electrical/thermal conductivities and lowered mass permeabilities, with emphasis on the latest structural control strategies for tuning transport properties. Key applications of functional elastomer nanocomposites related to transport phenomena are also introduced. Overall, this review summarizes the state of the art in the design and performance enhancement of elastomer nanocomposites based on the relationships between their structures and transport properties, governed by the components/composition, interface/dispersion and fabrication.