The current and heat ‘flow’ in standard metals is diffusive with electron motion randomized by impurities. However, for ultra-clean metals, electrons can flow like water, and that flow is described by fluid dynamics equations. Although hypothesized in theory, this situation has been very elusive for decades. In the last decade, several experimental groups have found strong indications of this type of flow, especially in graphene-based devices. This review provides an overview of some of the major recent developments, both theoretical and experimental.