Autoregulation is the result of a basic property of vascular smooth muscle cells where transmural pressure modifies muscle tone. As a result, flow is kept more or less constant over a range of blood pressures. In foetal lambs autoregulation develops from 0.6 gestation, whereas in extremely preterm babies the evidence is conflicting. Static autoregulation, measuring at steady state, is developed with a lower threshold at or below 30 mm Hg. The upper limit has not been determined. Dynamic autoregulation, measuring before steady state, appears not to be operating in preterm babies. The reason for this discrepancy is unknown and the clinical relevance is uncertain. In term and preterm babies with hypoxic-ischaemic brain injury, or with arterial hypotension treated with dopamine static autoregulation has been found absent. For clinical practice the relation between pressure and blood flow is less important than the relation between arterial pCO(2) and blood flow.