Thalassaemias result from mutations of the globin genes that cause reduced or absent haemoglobin production and thus interfere with the critical function of oxygen delivery. They represent the most common single-gene disorders, with 4.83% of the world population carrying globin gene variants. Reduced or absent α-globin (α-thalassaemia) or β-globin (β-thalassaemia) leads to anaemia and multifaceted clinical syndromes. In this second of two reviews on the pathophysiology of haemoglobinopathies, we describe the clinical features, pathophysiology and molecular basis of α- and β-thalassaemias. We then discuss current targeted therapies, including the new oral iron chelators, which, along with chronic transfusions, constitute the mainstay of symptomatic therapy for the majority of patients. Finally, we describe potentially curative therapies, such as bone marrow transplant, and discuss some of the outstanding research studies and questions, including the upcoming field of gene therapy for β-thalassaemia. An accompanying article on haemoglobinopathies (Part I) focuses on sickle cell disease.