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Neurodegenerative disorders, including Alzheimer's (AD) and Parkinson's diseases (PD), are characterised by the formation of aberrant assemblies of misfolded proteins. The discovery of disease-modifying drugs for these disorders is challenging, in part because we still have a limited understanding of their molecular origins. In this review, we discuss how biophysical approaches can help explain the formation of the aberrant conformational states of proteins whose neurotoxic effects underlie these diseases. We discuss in particular models based on the transgenic expression of amyloid-β (Aβ) and tau in AD, and α-synuclein in PD. Because biophysical methods have enabled an accurate quantification and a detailed understanding of the molecular mechanisms underlying protein misfolding and aggregation in vitro, we expect that the further development of these methods to probe directly the corresponding mechanisms in vivo will open effective routes for diagnostic and therapeutic interventions.