  We study evolution of dark matter substructures, especially how they lose the
mass and change density profile after they fall in gravitational potential of
larger host halos. We develop an analytical prescription that models the
subhalo mass evolution and calibrate it to results of N-body numerical
simulations of various scales from very small (Earth size) to large (galaxies
to clusters) halos. We then combine the results with halo accretion histories,
and calculate the subhalo mass function that is physically motivated down to
Earth-mass scales. Our results --- valid for arbitrary host masses and
redshifts --- show reasonable agreement with those of numerical simulations at
resolved scales. Our analytical model also enables self-consistent calculations
of the boost factor of dark matter annhilation, which we find to increase from
tens of percent at the smallest (Earth) and intermediate (dwarfs) masses to a
factor of several at galaxy size, and to become as large as a factor of
$\sim$10 for the largest halos (clusters) at small redshifts. Our analytical
approach can accommodate substructures in the subhalos (sub-subhalos) in a
consistent framework, which we find to give up to a factor of a few enhancement
to the annihilation boost. Presence of the subhalos enhances the intensity of
the isotropic gamma-ray background by a factor of a few, and as the result, the
measurement by Fermi Large Area Telescope excludes the annihilation cross
section greater than $\sim$$4\times 10^{-26}$ cm$^3$ s$^{-1}$ for dark matter
masses up to $\sim$200 GeV.

Cosmology and Nongalactic Astrophysics;High Energy Astrophysical Phenomena