Several models have predicted that stars could form inside galactic outflows and that this would be a new major mode of galaxy evolution. Observations of galactic outflows have revealed that they host large amounts of dense and clumpy molecular gas, which provide conditions suitable for star formation. We have investigated the properties of the outflows in a large sample of galaxies by exploiting the integral field spectroscopic data of the large MaNGA-SDSS4 galaxy survey. We find that star formation occurs inside at least half of the galactic outflows in our sample. We also show that even if star formation is prominent inside many other galactic outflows, this may have not been revealed as the diagnostics are easily dominated by the presence of even faint AGN and shocks. If very massive outflows typical of distant galaxies and quasars follow the same scaling relations observed locally, then the star formation inside high-z outflows can be up to several 100 Msun/yr and could contribute substantially to the early formation of the spheroidal component of galaxies. Star formation in outflows can also potentially contribute to establishing the scaling relations between black holes and their host spheroids. Moreover, supernovae exploding on large orbits can chemically enrich in-situ and heat the circumgalactic and intergalactic medium. Finally, young stars ejected on large orbits may also contribute to the reionization of the Universe.