Hemoglobinopathies are genetic disorders caused by aberrant hemoglobin expression or structure changes, resulting in severe mortality and health disparities worldwide. Sickle cell disease (SCD) and β-thalassemia, the most common forms of hemoglobinopathies, are typically treated using transfusions and pharmacological agents. Allogeneic hematopoietic stem cell transplantation is the only curative therapy, but has limited clinical applicability. Although gene therapy approaches have been proposed based on the insertion and forced expression of wild-type or anti-sickling β-globin variants, safety concerns may impede their clinical application. A novel curative approach is nuclease-based gene correction, which involves the application of precision genome-editing tools to correct the disease-causing mutation. This review describes the development and potential application of gene therapy and precision genome-editing approaches for treating SCD and β-thalassemia. The opportunities and challenges in advancing a curative therapy for hemoglobinopathies are also discussed.