Acute myeloid leukaemia (AML) is a molecularly and clinically heterogeneous disease, and its incidence is increasing as the populations in Western countries age. Despite major advances in understanding the genetic landscape of AML and its impact on the biology of the disease, standard therapy has not changed significantly in the last three decades. Allogeneic haematopoietic stem cell transplantation remains the best chance for cure, but can only be offered to a minority of younger fit patients. Molecularly targeted drugs aiming at restoring apoptosis in leukaemic cells have shown encouraging activity in early clinical trials and some of these drugs are currently being evaluated in randomised controlled trials. In this review, we discuss the current development of drugs designed to trigger cell death in AML.