Recently the NANOGrav collaboration, (and also later the PPTA and EPTA collaborations), reported the possibility of a stochastic process affecting their pulsar dataset, which, if confirmed, could prove to be the first detection of a Stochastic Gravitational Waves Background (SGWB). One of the possible sources of SGWB could be primordial gravitational waves. In this context, I will analyze the possibility that such a signal can be explained by models of the early universe that predict a tensor spectrum with a positive spectral index. A naive extrapolation down to interferometer scales of the blue GW spectrum required to explain NANOGrav consistently with Cosmic Microwave Background (CMB) observations would strongly violate upper limits on the SGWB amplitude from LIGO/Virgo. In combination with the fact that there are over 19 decades in frequency between CMB and interferometer scales, this motivates us to move beyond the commonly adopted approximation of a pure power-law GW spectrum. We consider a broken power-law parametrization for the SGWB spectrum, which turns from blue to red above the break frequency: while phenomenological, this choice maps to various well-motivated early-Universe models. We briefly discuss the very bright prospects for testing these model with next-generation probes across the GW frequency landscape. In the end of the talk I also discuss a connection of the primordial gravitational waves analysis with the H0 tension problem.