The pulmonary circulation differs from the systemic in several important aspects, the most important being that pulmonary arteries constrict to moderate physiological (∼20–60 mmHg PO2) hypoxia, whereas systemic arteries vasodilate. This phenomenon is called hypoxic pulmonary vasoconstriction (HPV), and is responsible for maintaining the ventilation–perfusion ratio during localized alveolar hypoxia. In disease, however, global hypoxia results in a detrimental increase in total pulmonary vascular resistance, and increased load on the right heart. Despite many years of study, the precise mechanisms underlying HPV remain unresolved. However, as we argue below, there is now overwhelming evidence that hypoxia can stimulate several pathways leading to a rise in the intracellular Ca2+ concentration ([Ca2+]i) in pulmonary artery smooth muscle cells (PASMC). This rise in [Ca2+]i is consistently found to be relatively small, and HPV seems also to require rho kinase‐mediated Ca2+ sensitization. There is good evidence that HPV also has an as yet unexplained endothelium dependency. In this brief review, we highlight selected recent findings and ongoing controversies which continue to animate the study of this remarkable and unique response of the pulmonary vasculature to hypoxia.