Many peptides and proteins self-assemble into amyloid fibrils. Examples include mammalian and fungal prion proteins, polypeptides associated with human amyloid diseases, and proteins that may have biologically functional amyloid states. To understand the propensity for polypeptides to form amyloid fibrils and to facilitate rational design of amyloid inhibitors and imaging agents, it is necessary to elucidate the molecular structures of these fibrils. Although fibril structures were largely mysterious 15 years ago, a considerable body of reliable structural information about amyloid fibril structures now exists, with essential contributions from solid state nuclear magnetic resonance (NMR) measurements. This Account reviews results from our laboratories and discusses several structural issues that have been controversial. In many cases, the amino acid sequences of amyloid fibrils do not uniquely determine their molecular structures. Self-propagating, molecular-level polymorphism complicates the structure determination problem and can lead to apparent disagreements between results from different laboratories, particularly when different laboratories study different polymorphs. For 40-residue β-amyloid (Aβ₁₋₄₀) fibrils associated with Alzheimer's disease, we have developed detailed structural models from solid state NMR and electron microscopy data for two polymorphs. These polymorphs have similar peptide conformations, identical in-register parallel β-sheet organizations, but different overall symmetry. Other polymorphs have also been partially characterized by solid state NMR and appear to have similar structures. In contrast, cryo-electron microscopy studies that use significantly different fibril growth conditions have identified structures that appear (at low resolution) to be different from those examined by solid state NMR. Based on solid state NMR and electron paramagnetic resonance (EPR) measurements, the in-register parallel β-sheet organization found in β-amyloid fibrils also occurs in many other fibril-forming systems. We attribute this common structural motif to the stabilization of amyloid structures by intermolecular interactions among like amino acids, including hydrophobic interactions and polar zippers. Surprisingly, we have recently identified and characterized antiparallel β-sheets in certain fibrils that are formed by the D23N mutant of Aβ₁₋₄₀, a mutant that is associated with early-onset, familial neurodegenerative disease. Antiparallel D23N-Aβ₁₋₄₀ fibrils are metastable with respect to parallel structures and, therefore, represent an off-pathway intermediate in the amyloid fibril formation process. Other methods have recently produced additional evidence for antiparallel β-sheets in other amyloid-formation intermediates. As an alternative to simple parallel and antiparallel β-sheet structures, researchers have proposed β-helical structural models for some fibrils, especially those formed by mammalian and fungal prion proteins. Solid state NMR and EPR data show that fibrils formed in vitro by recombinant PrP have in-register parallel β-sheet structures. However, the structure of infectious PrP aggregates is not yet known. The fungal HET-s prion protein has been shown to contain a β-helical structure. However, all yeast prions studied by solid state NMR (Sup35p, Ure2p, and Rnq1p) have in-register parallel β-sheet structures, with their Gln- and Asn-rich N-terminal segments forming the fibril core.