Small-angle X-ray scattering (SAXS) has emerged as a key complementary technique in structural biology. The data can be used to calculate average structural properties such as particle size and molecular weight, generate low-resolution models, test high resolution structures and be used as input for complex, structure-based modelling. Importantly, however, the data is the product of an average across all orientations and populations of the particle of interest, leading to an enormous loss of information. Thus, analysis of SAXS data usually involves an attempt to solve an ill-posed inverse problem. Meaningful interpretation, free of over-fitting, can be extremely challenging. Indeed, the inexperienced practitioner can easily arrive at a conclusion that is only weakly supported by the experiment. In this thesis, we suggest that in order to maximize its reliability, SAXS data is best interpreted in terms of clear hypotheses based on previous data, which can be queried against the scattering in a predictable fashion. This conservative approach minimizes the impact of the inverse problem inherent in modelling from averaged data.In Chapter 1, we outline this principle in a published review, "Small-angle X-ray scattering for the discerning macromolecular crystallographer", originally written for the community of structural biologists who may be seeking to use SAXS in support of their own experiments and published inThe Australian Journal of Chemistry. We supplement this with a discussion of the theoretical basis of analysis and the assumptions inherent in the process, in Chapter 2. We then proceed in the main body of the thesis to demonstrate this principle across a series of case studies addressing both technically and biologically relevant questions, together covering the modelling of flexibility, the verification of high-resolution structures and the analysis of self-association, in plant, animal and bacterial systems.In Chapter 3, we first examine one of the most demanding modelling applications: a flexible system being described as an ensemble. We introduce methodology to test the robustness of moleculardynamics (MD)-SAXS solutions with respect to changes in the conformational pool, and find that for our test system, yeast importin-β, a range of different and sometimes mutually exclusive ensembles are able to reproduce the data equally well. We note that the extendedness and gross shape of the protein can be reasonably extracted, and that particular distributions can be ruled out with confidence. However, we show that it is not possible to infer the presence of any specific individual conformation or group of conformations.In Chapter 4, we address a technical issue relevant to all following chapters. The recent development of size-exclusion coupled SAXS (SEC-SAXS) has led to significant improvements in data quality and better control of problematic interparticle effects. However, the highly dilute and high-3 throughput nature of these data requires protocols and data processing decisions which have not yet...