Neutron stars are excellent observatories to test our present understanding of the theory of strong interacting matter at extreme conditions, and they offer an interesting interplay between nuclear processes and astrophysical observables. Conditions of matter inside neutron stars are very different from those one can find in Earth and, therefore, a good knowledge of the equation of state of dense matter is required to understand the properties of neutron stars. On the first part of this talk I will briefly review some of the general properties of these fascinating objects.
On the second part, I will revise the problem of the strong softening of
the EoS, and the consequent reduction of the maximum mass, induced by the presence of hyperons in the neutron star interior, a puzzle which has become more intringuing and difficult to solve due the recent measurements of the unusually high masses of the millisecond pulsars PSR J1903+0327 ($1.667\pm 0.021 M_\odot$), PSR J1614-2230 ($1.97 \pm 0.04 M_\odot$), and PSR J0348+0432 ($2.01 pm 0.04 M_\odot$). Finally, I will also examine the role of hyperons on the cooling properties of newly born neutron stars and on the so-called r-mode instability.