Transthyretin (TTR) is one of the many proteins that are known to misfold and aggregate (i.e., undergo amyloidogenesis) in vivo. The process of TTR amyloidogenesis causes nervous system and/or heart pathology. While several of these maladies are associated with mutations that destabilize the native TTR quaternary and/or tertiary structure, wild-type TTR amyloidogenesis also leads to the degeneration of postmitotic tissue. Over the past 20 years, much has been learned about the factors that influence the propensity of TTR to aggregate. This biophysical information led to the development of a therapeutic strategy, termed “kinetic stabilization,” to prevent TTR amyloidogenesis. This strategy afforded the drug tafamidis which was recently approved by the European Medicines Agency for the treatment of TTR familial amyloid polyneuropathy, the most common familial TTR amyloid disease. Tafamidis is the first and currently the only medication approved to treat TTR familial amyloid polyneuropathy. Here we review the biophysical basis for the kinetic stabilization strategy and the structure-based drug design effort that led to this first-in-class pharmacologic agent. Display omitted ► Wild-type and mutant TTRs cause amyloid diseases in humans. ► Amyloid formation requires tetramer dissociation (rate limiting) and monomer misfolding. ► TTR tetramers can be kinetically stabilized by binding small molecules. ► Tafamidis, a kinetic stabilizer of TTR, is the first drug approved to treat TTR amyloidosis.