The link between protein aggregation and neurodegenerative disease is well established. However, given the heterogeneity of species formed during the aggregation process, it is difficult to delineate details of the molecular events involved in generating pathological aggregates from those producing soluble monomers. As aberrant aggregates are possible pharmacological targets for the treatment of neurodegenerative diseases, the need to observe and characterise soluble oligomers has pushed traditional biophysical techniques to their limits, leading to the development of a plethora of new tools capable of detecting soluble oligomers with high precision and specificity. In this review, we discuss a range of modern biophysical techniques that have been developed to study protein aggregation, and give an overview of how they have been used to understand, in detail, the aberrant aggregation of amyloidogenic proteins associated with the two most common neurodegenerative disorders, Alzheimer's disease and Parkinson's disease.