In this review, we summarize our present knowledge of the behaviour of the mass-radius relationship from solar-type stars down to terrestrial planets, across the regime of substellar objects, brown dwarfs and giant planets. Particular attention is paid to the identification of the main physical properties or mechanisms responsible for this behaviour. Indeed, understanding the mechanical structure of an object provides valuable information about its internal structure, composition and heat content as well as its formation history. Although the general description of these properties is reasonably well mastered, disagreement between theory and observation in certain cases points to some missing physics in our present modelling of at least some of these objects. The mass-radius relationship in the overlaping domain between giant planets and low-mass brown dwarfs is shown to represent a powerful diagnostic to distinguish between these two different populations and shows once again that the present IAU distinction between these two populations at a given mass has no valid foundation. © 2009 American Institute of Physics.