Organic-inorganic perovskites are a class of solution-processed semiconductors holding promise for the realization of low-cost efficient solar cells and on-chip lasers. Despite the recent attention they have attracted, fundamental aspects of the photophysics underlying device operation still remain elusive. Here we use photoluminescence and transmission spectroscopy to show that photoexcitations give rise to a conducting plasma of unbound but Coulomb-correlated electron-hole pairs at all excitations of interest for light-energy conversion and stimulated optical amplification. The conductive nature of the photoexcited plasma has crucial consequences for perovskite-based devices: in solar cells, it ensures efficient charge separation and ambipolar transport while, concerning lasing, it provides a low threshold for light amplification and justifies a favourable outlook for the demonstration of an electrically driven laser. We find a significant trap density, whose cross-section for carrier capture is however low, yielding a minor impact on device performance.