Neutrino physics has reached the precision era. Terrestrial experiments are able to constrain most of the neutrino properties, but many unknowns remain, even in the standard neutrino scenario. Cosmological observations, on the other hand, provide strong limits on the absolute neutrino mass scale but are almost insensitive to oscillation parameters. Beyond the vanilla case, however, several models propose the existence of additional neutrino states or interactions. These would alter the observations at terrestrial experiments and the neutrino processes in the early universe. In this seminar we analyse a variety of scenarios (light sterile neutrinos, non-unitarity of the mixing matrix, non-standard neutrino-electron interactions), discussing how cosmological probes can complement the observations we obtain at Earth.