The correct development of blood vessels is crucial for all aspects of tissue growth and physiology in vertebrates. The formation of an elaborate hierarchically branched network of endothelial tubes, through either angiogenesis or vasculogenesis, relies on a series of coordinated morphogenic events, but how individual endothelial cells adopt specific phenotypes and how they coordinate their behaviour during vascular patterning is unclear. Recent progress in our understanding of blood vessel formation has been driven by advanced imaging techniques and detailed analyses that have used a combination of powerful in vitro, in vivo and in silico model systems. Here, we summarise these models and discuss their advantages and disadvantages. We then review the different stages of blood vessel development, highlighting the cellular mechanisms and molecular players involved at each step and focusing on cell specification and coordination within the network.