The aggregation of proteins into amyloid-like fibrils is seen in many neurodegenerative diseases. Recent years have seen much progress in our understanding of these misfolded protein inclusions, thanks to advances in techniques such as solid-state nuclear magnetic resonance (ssNMR) spectroscopy and cryogenic electron microscopy (cryo-EM). However, multiple repeat-expansion-related disorders have presented special challenges to structural elucidation. This review discusses the special role of ssNMR analysis in the study of protein aggregates associated with CAG repeat expansion disorders. In these diseases, the misfolding and aggregation affect mutant proteins with expanded polyglutamine segments. The most common disorder, Huntington's disease (HD), is connected to the mutation of the huntingtin protein. Since the discovery of the genetic causes for HD in the 1990s, steady progress in our understanding of the role of protein aggregation has depended on the integrative and interdisciplinary use of multiple types of structural techniques. The heterogeneous and dynamic features of polyQ protein fibrils, and in particular those formed by huntingtin N-terminal fragments, have made these aggregates into challenging targets for structural analysis. ssNMR has offered unique insights into many aspects of these amyloid-like aggregates. These include the atomic-level structure of the polyglutamine core, but also measurements of dynamics and solvent accessibility of the non-core flanking domains of these fibrils' fuzzy coats. The obtained structural insights shed new light on pathogenic mechanisms behind this and other protein misfolding diseases.