Post-transplant lymphoproliferative disorders (PTLDs) are a group of conditions that involve uncontrolled proliferation of lymphoid cells as a consequence of extrinsic immunosuppression after organ or haematopoietic stem cell transplant. PTLDs show some similarities to classic lymphomas in the non-immunosuppressed general population. The oncogenic Epstein–Barr virus (EBV) is a key pathogenic driver in many early-onset cases, through multiple mechanisms. The incidence of PTLD varies with the type of transplant; a clear distinction should therefore be made between the conditions after solid organ transplant and after haematopoietic stem cell transplant. Recipient EBV seronegativity and the intensity of immunosuppression are among key risk factors. Symptoms and signs depend on the localization of the lymphoid masses. Diagnosis requires histopathology, although imaging techniques can provide additional supportive evidence. Pre-emptive intervention based on monitoring EBV levels in blood has emerged as the preferred strategy for PTLD prevention. Treatment of established disease includes reduction of immunosuppression and/or administration of rituximab (a B cell-specific antibody against CD20), chemotherapy and EBV-specific cytotoxic T cells. Despite these strategies, the mortality and morbidity remains considerable. Patient outcome is influenced by the severity of presentation, treatment-related complications and risk of allograft loss. New innovative treatment options hold promise for changing the outlook in the future.