The aggregation of proteins and peptides into a variety of insoluble, and often non-native, aggregated states plays a central role in many devastating diseases. Analogous processes undermine the efficacy of polypeptide-based biological pharmaceuticals, but are also being leveraged in the design of biologically inspired self-assembling materials. This Trends article surveys the essential contributions made by recent solid-state NMR (ssNMR) studies to our understanding of the structural features of polypeptide aggregates, and how such findings are informing our thinking about the molecular mechanisms of misfolding and aggregation. A central focus is on disease-related amyloid fibrils and oligomers involved in neurodegenerative diseases such as Alzheimer’s, Parkinson’s and Huntington’s disease. SSNMR-enabled structural and dynamics-based findings are surveyed, along with a number of resulting emerging themes that appear common to different amyloidogenic proteins, such as their compact alternating short-β-strand/β-arc amyloid core architecture. Concepts, methods, future prospects and challenges are discussed.