Malignant neoplasms constitute a major burden of morbidity and mortality in the general population. This necessitates intense screening of transplant candidates and even closer surveillance of immunosuppressed solid organ recipients. Active malignancy is an exclusion criterion to solid organ transplantation, with few exceptions, namely localized hepatic neoplasms. Accelerated tumor progression characterizes post-transplantation malignancies. Intensified surveillance is justified in elevated rates, e.g., of skin cancer and virus-associated neoplasms, especially Epstein-Barr virus-associated post-transplantation lymphoproliferative disease (PTLD). Renal cell cancer rates rise after kidney transplantation, predominantly affecting the native kidneys. Chemotherapeutic dose adjustments for renal and hepatic function pharmacokinetic interactions are frequent and require active monitoring. Immunotherapies pose new challenges by induction of allograft rejection. Data on management of immunosuppression are emerging. Individualized concepts need to take into account therapeutic options of both anti-cancer therapy and organ replacement.