Protein fibrillation is first and foremost a structural phenomenon. Adequate structural investigation of the central conformational individuals of the fibrillation process is however exceedingly difficult. This is due to the nature of the process, which may be described as a dynamically evolving equilibrium between a large number of structural species. These are furthermore of highly diverging sizes and present in very uneven amounts and timeframes. Different structural methods have different strengths and limitations. These, and in particular recent advances within solution analysis of the undisturbed equilibrium using small angle X-ray scattering, are reviewed here.