Amyloid fibrils are structurally defined as fibrillar polypeptide aggregates with a characteristic cross-β structure. Such fibrils can be formed by certain polypeptide sequences in the human body and by numerous polypeptide sequences in vitro. All amyloid fibrils possess a structural spine that is formed by a cross-β structure. This structure is stabilized by hydrogen bonds between the polypeptide backbone. In recent years, various biophysical techniques, such as X-ray crystallography, solid state nuclear magnetic resonance spectroscopy and electron cryo-microscopy have provided insights into the structural organization of amyloid fibrils. This review presents an overview of important results obtained with these methods.