 This study will enroll people with thalassemia who have pulmonary hypertension and a control group of people with thalassemia who do not have pulmonary hypertension. People with thalassemia and pulmonary hypertension will attend a baseline study visit at which time they will undergo the following procedures: medical history and medical record review; physical exam; a 6-minute walk test, which will measure how far participants can walk in 6 minutes; an echocardiogram to obtain images of the heart; blood collection; and for females, a urine collection. Participants will then begin taking sildenafil three times a day for 12 weeks. At study visits at Weeks 2, 4, and 8, participants will undergo repeat baseline testing, and some participants will take part in an exhaled nitric oxide test. At Week 12, participants will also undergo lung function testing and a chest magnetic resonance imaging MRI procedure. 