Amyloidoses include a large variety of local and systemic diseases that share the common feature of protein unfolding or refolding into amyloid fibrils. The most studied amyloids are those directly involved in neurodegenerative diseases, while others, such as those formed by insulin, are surprisingly far less studied. Insulin is a very important polypeptide that plays a variety of biological roles and, first and foremost, is at the basis of the therapy of diabetic patients. It is well-known that it can form fibrils at the site of injection, leading to inflammation and immune response, in addition to other side effects. In this concise review, we analyze the current knowledge on insulin fibrillation, with a focus on the development of peptide-based inhibitors, which are promising candidates for their biocompatibility but still pose challenges to their effective use in therapy.