Characterisation and quantification of tissue structures is limited by sectioning-induced artefacts and by the difficulties of visualising and segmenting 3D volumes. Here we demonstrate that, even in the absence of X-ray contrast agents, X-ray computed microtomography (microCT) and nanotomography (nanoCT) can circumvent these problems by rapidly resolving compositionally discrete 3D tissue regions (such as the collagen-rich adventitia and elastin-rich lamellae in intact rat arteries) which in turn can be segmented due to their different X-ray opacities and morphologies. We then establish, using X-ray tomograms of both unpressurised and pressurised arteries that intra-luminal pressure not only increases lumen cross-sectional area and straightens medial elastic lamellae but also induces profound remodelling of the adventitial layer. Finally we apply microCT to another human organ (skin) to visualise the cell-rich epidermis and extracellular matrix-rich dermis and to show that conventional histological and immunohistochemical staining protocols are compatible with prior X-ray exposure. As a consequence we suggest that microCT could be combined with optical microscopy to characterise the 3D structure and composition of archival paraffin embedded biological materials and of mechanically stressed dynamic tissues such as the heart, lungs and tendons.