The utility of concrete as a cost-effective, durable structural material depends largely on its fracture properties. Improved understandings of the physical bases and scaling of concrete fracture are needed to meet the growing expectations and constraints on concrete usage in high-performance applications, and to develop alternative cementitious materials for reduced environmental load. This paper reviews relevant knowledge of fracture processes in concrete, with a particular focus on ways new 3D measurements may be coupled with discrete modelling approaches. The microstructure of concrete is briefly reviewed in the context of the physical processes that dictate fracture properties. We advocate a modelling approach where, to the extent possible, a direct correspondence is made between measured material structure and the structures explicitly represented by numerical models. This correspondence is made by utilizing x-ray microtomography, a high-resolution 3D imaging technique, and lattice models that mimic physical structure and processes. 3D image analysis provides us with quantitative measurements of internal damage progression. 3D lattice simulations offer the potential for extracting additional knowledge from these high-fidelity measurements.