  In this article we briefly review our recent results on evolution and
properties of isolated neutron stars (INSs) in the Galaxy.
  As the first step we calculate a {\it census} of INSs in our Galaxy.
  We infer a lower bound for the mean kick velocity of NSs, $ <V> \sim
$(200-300) ${\rm km s^{-1}}$. The same conclusion is reached for both a
constant magnetic field ($B\sim 10^{12}$ G) and for a magnetic field decaying
exponentially with a timescale $\sim 10^9$ yr. These results, moreover,
constrain the fraction of low velocity stars, which could have escaped pulsar
statistics, to $\sim$few percents.
  Then we show that the range of minimum value of magnetic moment, $\mu_b$:
$\sim 10^{29.5}\ge \mu_b \ge 10^{28} {\rm G} {\rm cm}^3$, and the
characteristic decay time, $t_d$: $\sim 10^8\ge t_d \ge 10^7 {\rm yrs}$, can be
excluded assuming the standard initial magnetic momentum, $\mu_0=10^{30} {\rm
G} {\rm cm}^3$, if accreting INSs are observed. For these parameters an INS
would never reach the stage of accretion from the interstellar medium even for
a low space velocity of the star and high density of the ambient plasma. The
range of excluded parameters increases for lower values of $\mu_0$.
  It is shown that old accreting INSs become more abundant than young cooling
INSs at X-ray fluxes below $\sim 10^{-13}$ erg cm$^{-2}$ s$^{-1}$. We can
predict that about one accreting INS per square degree should be observed at
the {\it Chandra} and {\it Newton} flux limits of $\sim 10^{-16}$ erg cm$^{-2}$
s$^{-1}.$ The weak {\it ROSAT} sources, associated with INSs, can be young
cooling objects, if the NSs birth rate in the solar vicinity during the last
$\sim 10^6$ yr was much higher than inferred from radiopulsar observations.
