A microcomputed tomography (μCT) facility and computational infrastructure developed at the Department of Applied Mathematics at the Australian National University is described. The current experimental facility is capable of acquiring 3D images made up of 20003 voxels on porous specimens up to 60 mm diameter with resolutions down to 2 μm. This allows the three-dimensional (3D) pore-space of porous specimens to be imaged over several orders of magnitude. The computational infrastructure includes the establishment of optimised and distributed memory parallel algorithms for image reconstruction, novel phase identification, 3D visualisation, structural characterisation and prediction of mechanical and transport properties directly from digitised tomographic images. To date over 300 porous specimens exhibiting a wide variety of microstructure have been imaged and analysed. In this paper, analysis of a small set of porous rock specimens with structure ranging from unconsolidated sands to complex carbonates are illustrated. Computations made directly on the digitised tomographic images have been compared to laboratory measurements. The results are in excellent agreement. Additionally, local flow, diffusive and mechanical properties can be numerically derived from solutions of the relevant physical equations on the complex geometries; an experimentally intractable problem. Structural analysis of data sets includes grain and pore partitioning of the images. Local granular partitioning yields over 70,000 grains from a single image. Conventional grain size, shape and connectivity parameters are derived. The 3D organisation of grains can help in correlating grain size, shape and orientation to resultant physical properties. Pore network models generated from 3D images yield over 100000 pores and 200000 throats; comparing the pore structure for the different specimens illustrates the varied topology and geometry observed in porous rocks. This development foreshadows a new numerical laboratory approach to the study of complex porous materials.