Alpha-synuclein (aS) and its aggregation properties are central in the development and spread of Parkinson's disease. Point mutations and multiplications of the SNCA gene encoding aS cause autosomal dominant forms of the disorder. Moreover, protein inclusions found in the surviving neurons of parkinsonian brains consist mainly of a fibrillar form of aS. Aggregates of aS, which form a transient, complex and heterogeneous ensemble, participate in a wide variety of toxic mechanisms that may be amplified by aS spreading among neighbouring neurons. Recently, significant effort has been directed into the study of the aS aggregation process and the impact of aS aggregates on neuron survival. In this review, we present state-of-the-art biophysical studies on the aS aggregation process in vitro and in cellular models. We comprehensively review the new insights generated by the recent biophysical investigations, which could provide a solid basis from which to design future biomedical studies. The diverse cellular models of aS toxicity and their potential use in the biophysical investigation are also discussed.