It is often assumed that local increases of tissue blood flow are mediated by relaxation of arteriolar smooth muscle but in many tissues, including the brain, heart, kidney and pancreas, capillary control of blood flow by contractile pericytes also occurs. In the brain, most of the adjustable resistance of the intra-cerebral vasculature is located in capillaries. I will demonstrate that neuronal activity mainly increases cerebral blood flow by dilating capillaries via pericytes, that this involves signalling via astrocytes, and that dilation of capillaries and of arterioles are mediated by different messengers. In the brain, heart and kidney, ischaemia leads to pericytes constricting, producing a long-lasting decrease of blood flow after ischaemia. Constriction of cerebral capillaries by pericytes also occurs at an early stage of Alzheimer’s Disease, when it is expected to amplify the production of amyloid beta. The SARS-CoV-2 virus causing Covid-19 binds to ACE2 on cerebral pericytes and amplifies angiotensin II – evoked pericyte constriction by decreasing ACE2 function. Thus, awareness of the possibility of pericyte-mediated capillary constriction reveals new therapeutic targets to increase blood flow in numerous pathologies.