Neutron stars are natural laboratories to test physics under extreme conditions, hardly reproducible in different astrophysical and Earth environments. From the behavior of strong interactions at supranuclear densities, to the features of gravitational phenomena in their surroundings, neutron star are magnifying lenses of fundamental forces. In this talk we will review the status of the modelling and of the phenomenology of neutron stars in, and beyond GR. We will describe the stellar macroscopic features, their connection with the underlying equation of state, and the constraints available so far from the gravitational wave and the electromagnetic band. Finally we will discuss extensions of neutron star models to alternative theories of gravity as well as the signatures able to distinguish them from their GR counterparts.