The purpose of this research is to see if taking part in structured exercise training will improve the ability to exercise, the function of the heart, and the function of the blood vessels that supply the lungs in patients with heart failure and pulmonary hypertension. After enrollment all patients will complete exercise testing. Patients will be randomized to either 10 weeks of exercise training (3 times per week) or will continue standard medical care. All patients will undergo detailed exercise testing before and after the intervention.