“Cardiac amyloidosis” is the term commonly used to reflect the deposition of abnormal protein amyloid in the heart. This process can result from several different forms, most commonly from light-chain (AL) amyloidosis and transthyretin (ATTR) amyloidosis, which in turn can represent wild-type (ATTRwt) or genetic form. Regardless of the origin, cardiac involvement is usually associated with poor prognosis, especially in AL amyloidosis. Although several treatment options, including chemotherapy, exist for different forms of the disease, cardiac transplantation is increasingly considered. However, high mortality on the transplantation list, typical for patients with amyloidosis, and suboptimal post-transplant outcomes are major issues. We are reviewing the literature and summarizing pros and cons of listing patients with amyloidosis for cardiac or combine organ transplant, appropriate work-up, and intermediate and long-term outcomes. Both AL and ATTR amyloidosis are included in this review.