Familial amyloid polyneuropathies (FAPs) are a group of life-threatening multisystem disorders transmitted as an autosomal dominant trait. Nerve lesions are induced by deposits of amyloid fibrils, most commonly due to mutated transthyretin (TTR). Less often the precursor of amyloidosis is mutant apolipoprotein A-1 or gelsolin. The first identified cause of FAP—the TTR Val30Met mutation—is still the most common of more than 100 amyloidogenic point mutations identified worldwide. The penetrance and age at onset of FAP among people carrying the same mutation vary between countries. The symptomatology and clinical course of FAP can be highly variable. TTR FAP typically causes a nerve length-dependent polyneuropathy that starts in the feet with loss of temperature and pain sensations, along with life-threatening autonomic dysfunction leading to cachexia and death within 10 years on average. TTR is synthesised mainly in the liver, and liver transplantation seems to have a favourable effect on the course of neuropathy, but not on cardiac or eye lesions. Oral administration of tafamidis meglumine, which prevents misfolding and deposition of mutated TTR, is under evaluation in patients with TTR FAP. In future, patients with FAP might benefit from gene therapy; however, genetic counselling is recommended for the prevention of all types of FAP.