For several different proteins an apparent correlation has been observed between the propensity for dimerization by domain-swapping and the ability to aggregate into amyloid-like fibrils. Examples include the disease-related proteins β 2-microglobulin and transthyretin. This has led to proposals that the amyloid-formation pathway may feature extensive domain swapping. One possible consequence of such an aggregation pathway is that the resulting fibrils would incorporate structural elements that resemble the domain-swapped forms of the protein and, thus, reflect certain native-like structures or domain-interactions. In magic angle spinning solid-state NMR-based and other structural studies of such amyloid fibrils, it appears that many of these proteins form fibrils that are not native-like. Several fibrils, instead, have an in-register, parallel conformation, which is a common amyloid structural motif and is seen, for instance, in various prion fibrils. Such a lack of native structure in the fibrils suggests that the apparent connection between domain-swapping ability and amyloid-formation may be more subtle or complex than may be presumed at first glance.