Prions are infectious proteins best known as the agent of BSE and new variant Creutzfeldt-Jakob disease. Their infectious form has been identified as a beta-sheet-rich molecular aggregate termed amyloid fibril. Additionally, amyloid formation is eponymous for a group of diseases (Amyloidoses) that includes Alzheimer and Parkinson's. Yet amyloid fibrils remain structurally poorly characterized as they are neither accessible by X-ray crystallography nor solution NMR. My PhD work comprises structural studies of amyloid fibrils of prions and the development of new tools for structure determination by solid-state NMR (ssNMR), currently the sole source for atomic-level structural information about amyloids. The central piece of this work was the calculation of the structure of HET-s(218-289). This is the first known structure of an amyloid core of a prion in general. It enabled the following diverse studies on a range of subjects such as non-infectious fibrils of HET-s, a study on a homologue of HET-s and a structural study of bacterial inclusion bodies.