Pulmonary hypertension is a progressive and often fatal cardiopulmonary condition characterised by increased pulmonary arterial pressure, structural changes in the pulmonary circulation, and the formation of vaso-occlusive lesions. These changes lead to increased right ventricular afterload, which often progresses to maladaptive right ventricular remodelling and eventually death. Pulmonary arterial hypertension represents one of the most severe and best studied types of pulmonary hypertension and is consistently targeted by drug treatments. The underlying molecular pathogenesis of pulmonary hypertension is a complex and multifactorial process, but can be characterised by several hallmarks: inflammation, impaired angiogenesis, metabolic alterations, genetic or epigenetic abnormalities, influence of sex and sex hormones, and abnormalities in the right ventricle. Current treatments for pulmonary arterial hypertension and some other types of pulmonary hypertension target pathways involved in the control of pulmonary vascular tone and proliferation; however, these treatments have limited efficacy on patient outcomes. This review describes key features of pulmonary hypertension, discusses current and emerging therapeutic interventions, and points to future directions for research and patient care. Because most progress in the specialty has been made in pulmonary arterial hypertension, this review focuses on this type of pulmonary hypertension. The review highlights key pathophysiological concepts and emerging therapeutic directions, targeting inflammation, cellular metabolism, genetics and epigenetics, sex hormone signalling, bone morphogenetic protein signalling, and inhibition of tyrosine kinase receptors.