The formation of blood cells such as erythrocytes (erythropoiesis), leukocytes (leukopoiesis), and platelets (thrombopoiesis) from pluripotent stem cells. Normally, hematopoiesis takes place in the bone marrow. However, hematopoiesis occurs in sites other than the bone marrow (extramedullary hematopoiesis) such as the liver and spleen during normal fetal development, in chronic, severe anemia, and in some hematological malignancies (e.g., Hodgkin lymphoma).