Transthyretin amyloidosis represents a spectrum of clinical syndromes that, in all cases except senile systemic amyloidosis, are dependent on the mutation present in the transthyretin (TTR) protein. Although the role of amyloid deposits in the pathogenesis of the disease is not clear, preventing their formation or promoting their disaggregation is necessary to control the development of clinical symptoms. The design of therapies aiming at preventing amyloid formation or promoting its dissociation requires detailed knowledge of the fibrils' molecular structure and a complete view about the factors responsible for protein aggregation. This review is focused on the structural studies, performed on amyloid fibrils and amyloidogenic TTR variants, aiming at understanding the aggregation mechanism as well as the atomic structure of the fibril assembly, Based on the available information possible therapies are also surveyed.