It is by now well understood that large sprite discharges at the low air densities of the mesosphere are physically similar to small streamer discharges in air at standard temperature and pressure. This similarity is based on Townsend scaling with air density. First the theoretical basis of Townsend scaling and a list of six possible corrections to scaling are discussed; then the experimental evidence for the similarity between streamers and sprites is reviewed. We then discuss how far present sprite and streamer theory has been developed, and we show how streamer experiments can be interpreted as sprite simulations. We review those results of recent streamer research that are relevant for sprites and other forms of atmospheric electricity and discuss their implications for sprite understanding. These include the large range of streamer diameters and velocities and the overall 3D morphology with branching, interaction and reconnection, the dependence on voltage and polarity, the electron energies in the streamer head and the consecutive chemical efficiency and hard radiation. New theoretical and experimental results concern measurements of streamer spectra in air, the density dependence of streamer heating (hot leaders are unlikely at 80 km altitude and cold streamers are unlikely in liquids), and a discussion of the influence of magnetic fields on thermal electrons or on energetic electrons in streamers or sprites.