Amyloid fibrils are ordered protein aggregates and a hallmark of many severe neurodegenerative diseases. Amyloid fibrils form through primary nucleation from monomeric protein, grow through monomer addition and proliferate through fragmentation or through the nucleation of new fibrils on the surface of existing fibrils (secondary nucleation). It is currently still unclear how amyloid fibrils initially form in the brain of affected individuals and how they are amplified. A given amyloid protein can sometimes form fibrils of different structure under different solution conditions in vitro, but often fibrils found in patients are highly homogeneous. These findings suggest that the processes that amplify amyloid fibrils in vivo can in some cases preserve the structural characteristics of the initial seed fibrils. It has been known for many years that fibril growth by monomer addition maintains the structure of the seed fibril, as the latter acts as a template that imposes its fold on the newly added monomer. However, for fibrils that are formed through secondary nucleation it was, until recently, not clear whether the structure of the seed fibril is preserved. Here we review the experimental evidence on this question that has emerged over the last years. The overall picture is that the fibril strain that forms through secondary nucleation is mostly defined by the solution conditions and intrinsic structural preferences, and not by the seed fibril strain.