Amyloidosis comprises a diverse group of diseases characterized by misfolding of precursor proteins which eventually form amyloid aggregates and preceding intermediaries, which are deposited in target tissues causing progressive organ damage. In all forms of amyloidosis, vital organs may fail; depending on the specific amyloidosis type, this may occur rapidly or progress slowly. Beyond therapies to reduce the precursor protein (chemotherapy for light chain [AL] amyloidosis, anti-inflammatory therapy in serum A amyloidosis [AA], and antisense RNA therapy in transthyretin amyloidosis [ATTR]), organ transplantation may also be a means to reduce amyloidogenic protein, e.g., in types of amyloidosis in which the variant precursor is produced by the liver. Heart transplantation is a life-saving approach to the treatment of patients with advanced cardiac amyloidosis; however, amyloidosis may still be considered a contraindication to the procedure despite data supporting improved outcomes, similar to patients with other indications. Kidney transplantation is associated with particularly favorable outcomes in patients with amyloidosis, especially if the precursor protein has been eliminated. Overall, outcomes of solid organ transplantation are improving, but more data are needed to refine the selection criteria and the timing for organ transplantation, which should be performed in highly experienced centers involving multidisciplinary teams with close patient follow-up to detect amyloid recurrence.