Radioquiet isolated neutron stars: old and young, nearby and far away, dim and very dim

We briefly discuss the evolutionary path and observational appearance of isolated neutron stars (INSs) focusing on radioquiet objects. There are many reasons to believe that these sources are extremely elusive once the star surface has cooled down: their high spatial velocities, the long propeller stage and/or the very low accretion efficiency. We describe recent population synthesis models of close-by young INSs, highlighting the major difficulties encountered in the past by these simulations in reproducing the observed properties of known sources. As we show, a likely possibility is that most of the INSs in the Solar proximity are young (less than few Myrs) neutron stars born in the Gould Belt. To stay hot enough and sustain X-ray emission for a time $\approx 1$ Myr, they probably need to be low- to medium-massive, with $M$ less than$\sim 1.35M_{\odot }$.