The NANOGrav pulsar timing collaboration has recently reported strong evidence for a new stochastic common-spectrum process affecting the pulsar timing residuals in its 12.5-year data set. If confirmed in the future, this signal may turn out to be the first glimpse of a stochastic gravitational-wave background at nanohertz frequencies. In this talk, I will demonstrate that the NANOGrav data readily admit an interpretation in terms of gravitational waves emitted by a network of cosmic strings. An intriguing possibility for the origin of this network is the cosmological breaking of baryon-minus-lepton number, B-L. In this scenario, the NANOGrav signal is linked to the dynamics of the early Universe close to the energy scale of grand unification and has important implications for neutrino physics and leptogenesis. This talk is based on 1305.3392, 1912.03695, 2004.02889, 2009.06607, 2009.10649 in collaboration with many great collaborators.