  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$\sim 1.35 M_\odot$.
