Asphaltenes are an important class of complex carbon-rich molecules found in crude oil. Their chemical structure varies depending on the geological source but generally comprises fused aromatic rings, aliphatic substituents and heteroatom functionality, which results in a strong tendency to aggregate and phase separate within crude oil. Asphaltene ‘drop-out’ owing to phase separation is a major problem spanning crude oil extraction, refining and application. More specifically, the build-up of asphaltene deposits can reduce the permeability of porous rock formations, block oil pipelines, and compromise the efficiency of marine engines. This major technical problem is compounded by the fact that the chemical composition, structure and colloidal behavior of asphaltenes varies significantly depending on the origin of the crude oil and the conditions employed for its refinement. As a result, there has been a concerted effort to (i) understand the morphology of asphaltene dispersions, (ii) identify the underlying mechanism(s) that lead to asphaltene ‘drop-out’ and hence (iii) design stabilizers to maintain colloid stability and/or minimize ‘drop-out’. In principle, imaging techniques can be used to visualize the asphaltene aggregates while light scattering can provide particle size information, but these techniques only provide rather limited structural information. Asphaltene aggregation involves several steps and results in highly hierarchical structures including primary nanoaggregates, clusters, and fractal structures, with characteristic length scales ranging from a few angstroms to several microns. In this review article, the use of small-angle scattering (SAS) and X-ray diffraction (XRD) to characterize asphaltene powders, dispersions and aggregates over the past six decades is summarized. These powerful techniques provide a wealth of structural information about molecular stacking, particle size and morphology, and fractal dimensions.