Pulmonary hypertension (PH) associated with left heart disease (PH-LHD) is the most common type of PH, but its natural history is not well understood. PH-LHD is diagnosed by right heart catheterisation with a mean pulmonary arterial pressure ≥25 mmHg and a pulmonary capillary wedge pressure >15 mmHg. The primary causes of PH-LHD are left ventricular dysfunction of systolic and diastolic origin, and valvular disease. Prognosis is poor and survival rates are low. Limited progress has been made towards specific therapies for PH-LHD, and management focuses on addressing the underlying cause of the disease with supportive therapies, surgery and pharmacological treatments. Clinical trials of therapies for pulmonary arterial hypertension in patients with PH-LHD have thus far been limited and have provided disappointing or conflicting results. Robust, long-term clinical studies in appropriate target populations have the potential to improve the outlook for patients with PH-LHD. Herein, we discuss the knowledge gaps in our understanding of PH-LHD, and describe the current unmet needs and challenges that are faced by clinicians when identifying and managing patients with this disease.