Transthyretin kinetic stabilizers are used as first-line drug therapy for transthyretin amyloid polyneuropathy mostly in patients unsuitable for liver transplantation. The two drugs prescribed in clinical practice are Tafamidis and Diflunisal. The European Medicines Agency approved Tafamidis for this prescription in 2011 and 2019 American Food and Drug Association also registered it for the same use. Diflunisal is a non-steroidal anti-inflammatory drug but its structural similarities to Tafamidis determine its “off-label” use for such clinical conditions. This review article represents the various analytical methods available in published literature for the determination of Tafamidis and Diflunisal in bulk drugs, pharmaceutical formulations, and biological matrices. Detailed information about all developed quantitative methods consisting of spectrophotometry, spectrofluorimetry, high-performance liquid chromatography with ultraviolet, fluorescence or diode array detection, liquid chromatography-tandem mass spectrometry, and voltammetry is provided and can be effectively used in the development of new analytical procedures and routine drug manufacturing or clinical practice.