In this paper we briefly review our recent results on evolution and properties of isolated neutron stars ( INSs ) in the Galaxy .

As the first step we discuss stochastic period evolution of INSs .
We briefly discuss how an INS ’ s spin period evolves under influence of interaction with turbulized interstellar medium .

To investigate statistical properties of the INS population we calculate a census of INSs in our Galaxy .
We infer a lower bound for the mean kick velocity of NSs , < V > \sim ( 200-300 ) { 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 NSs , which could have escaped pulsar statistics , to \sim few percents .

Then we show that for exponential field decay the range of minimum value of magnetic moment , \mu _ { b } : \sim 10 ^ { 29.5 } \geq \mu _ { b } \geq 10 ^ { 28 } { G } { cm } ^ { 3 } , and the characteristic decay time , t _ { d } : \sim 10 ^ { 8 } \geq t _ { d } \geq 10 ^ { 7 } { yrs } , can be excluded assuming the standard initial magnetic momentum , \mu _ { 0 } = 10 ^ { 30 } { G } { 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 Chandra and Newton flux limits of \sim 10 ^ { -16 } erg cm ^ { -2 } s ^ { -1 } . The weak 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 .