Pulmonary hypertension encompasses a range of conditions directly or indirectly leading to elevated pressures within the pulmonary arteries. Five main groups of pulmonary hypertension are recognized, all defined by a mean pulmonary artery pressure of >20 mmHg: pulmonary arterial hypertension (rare), pulmonary hypertension associated with left-sided heart disease (very common), pulmonary hypertension associated with lung disease (common), pulmonary hypertension associated with pulmonary artery obstructions, usually related to thromboembolic disease (rare), and pulmonary hypertension with unclear and/or multifactorial mechanisms (rare). At least 1% of the world’s population is affected, with a greater burden more likely in low-income and middle-income countries. Across all its forms, pulmonary hypertension is associated with adverse vascular remodelling with obstruction, stiffening and vasoconstriction of the pulmonary vasculature. Without proactive management this leads to hypertrophy and ultimately failure of the right ventricle, the main cause of death. In older individuals, dyspnoea is the most common symptom. Stepwise investigation precedes definitive diagnosis with right heart catheterization. Medical and surgical treatments are approved for pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension. There are emerging treatments for other forms of pulmonary hypertension; but current therapy primarily targets the underlying cause. There are still major gaps in basic, clinical and translational knowledge; thus, further research, with a focus on vulnerable populations, is needed to better characterize, detect and effectively treat all forms of pulmonary hypertension.