Hemoglobinopathies, namely β-thalassemia and sickle cell disease (SCD), are hereditary diseases, characterized by molecular genetic aberrations in the beta chains of hemoglobin. These defects affect the normal production of hemoglobin with severe anemia due to less or no amount of beta globins in patients with β-thalassemia (quantitative disorder), while SCD is a serious disease in which a mutated form of hemoglobin distorts the red blood cells into a crescent shape at low oxygen levels (qualitative disorder). Despite the revolutionary progress in recent years with the approval of gene therapy and gene editing for specific patients, there is an unmet need for highlighting the mechanisms influencing hemoglobin production and for the development of novel drugs and targeted therapies. The identification of the transcription factors and other genetic modifiers of hemoglobin expression is of utmost importance for discovering novel therapeutic approaches for patients with hemoglobinopathies. The aim of this review is to describe these complex molecular mechanisms and pathways affecting hemoglobin expression and to highlight the relevant investigational approaches or pharmaceutical interventions focusing on restoring the hemoglobin normal function by linking the molecular background of the disease with the clinical perspective. All the associated drugs increasing the hemoglobin expression in patients with hemoglobinopathies, along with gene therapy and gene editing, are also discussed.