Down syndrome is a common congenital disorder affecting ~1/1000 live births. Newborns and children with Down syndrome may present with many haematological problems. In addition, benign abnormalities of the blood count and blood film, which may manifest at any age, population‐based and cancer‐based registries and clinical trials suggest there is a ~12‐fold increased risk of acute lymphoblastic leukaemia in the age group of 5–30 years that rises to ~40‐fold in children younger than 5 years, and that there is a ~150‐fold increased risk of acute myeloid leukaemia in children younger than 5 years. There is also a virtually unique predisposition to a transient neonatal leukaemia, known as transient abnormal myelopoiesis. Deaths from leukaemia, in part, account for the excess mortality associated with Down syndrome. This article reviews the clinical presentation and the progress made in the management of these disorders over the past decade. It also briefly considers the recent exciting scientific advances that have potential to transform management of leukaemia in children with Down syndrome and also have implications for management of childhood leukaemia more generally.