In recent years the issues of protein stability, folding and aggregation have become central in several pathological conditions and in particular in amyloid diseases. Here, we review the recent developments on the molecular mechanisms of amyloid formation by transthyretin (TTR), in particular, in what concerns to protein conformational stability, protein folding and aggregation. Transthyretin has been implicated in pathologies such as senile systemic amyloidosis (SSA), familial amyloid polyneuropathy (FAP) and familial amyloid cardiomyopathy (FAC) which are characterized by extracellular deposition of insoluble amyloid fibrils. SSA is generally a mild disorder and affects predominantly individuals over 80 years of age. In contrast, FAP is an autossomal dominant lethal disease, characterized by peripheral neuropathy, which may affect individuals from their twenties. While in SSA WT-TTR and its fragments are the major constituents of the amyloid fibrils, in FAP and FAC the amyloid fibrils are mostly constituted by variants of TTR. Today, more than 80 TTR mutations throughout the TTR sequence are known. Transthyretin is a homotetrameric protein found in the plasma and in the cerebral-spinal fluid, it is synthesized in the liver and in the choroid plexus of the brain, it has a total molecular mass of 55kDa and a high percentage of β-sheet. Current views on amyloid fibril formation by TTR state that, depending on the protein variant or solution conditions, the native tetrameric protein might dissociate to non-native or partially unfolded monomeric (or even dimeric) species with a high tendency for ordered aggregation into soluble oligomers which grow into insoluble oligomers and eventually mature amyloid fibrils. Thus, issues such as dissociation thermodynamics and dissociation kinetics of the native tetrameric TTR and thermodynamic stability and conformational fluctuations of the non-native TTR molecular species are essential in determining the amyloidogenic potential of different TTR variants. In addition, several other cellular and tissue factors must be involved in modulating the penetrance and age of onset of amyloid pathologies by TTR.