A number of neurodegenerative disorders, such as Alzheimer's disease and Parkinson's disease, involve the formation of protein aggregates. The primary constituent of these aggregates belongs to a unique class of heteropolymers known as intrinsically disordered proteins (IDPs). While many proteins fold to a unique conformation that is determined by their amino acid sequence, IDPs do not adopt a single well-defined conformation in solution. Instead, they populate a heterogeneous set of conformers under physiological conditions. Despite this intrinsic propensity for disorder, a number of these proteins can form ordered aggregates both in vitro and in vivo. As the formation of these aggregates may play an important role in disease pathogenesis, a detailed structural characterization of these proteins and their mechanism of aggregation is of critical importance. However, new methods are needed to understand the diversity of structures that make up the unfolded ensemble of these systems. In this review, we discuss recent advances in the structural analysis and modeling of IDPs involved in neurodegenerative diseases. While there are challenges in both the experimental characterization and the modeling of such proteins, a comprehensive understanding of the structure of IDPs will likely facilitate the development of effective therapies for a number of neurodegenerative diseases.