With neutrinos we can investigate physics at energies spanning at least 30 orders of magnitude: from the very low radio frequencies tested by 21 cm cosmology to the grand-unified scale tested, for example, by leptogenesis. Together with some very well established processes such as neutrino mixing, I will discuss more speculative phenomenological effects that, thanks to neutrino physics, could provide signatures of new physics in the next years in a large variety of experiments: from colliders to cosmology, from neutrino oscillations to astrophysical probes. Finally, I will discuss some examples of models that might realise grand-unification and/or address the flavour problem.