  We present recent results in three-flavor chiral perturbation theory at
finite isospin $\mu_I$ and strangeness $\mu_s$ chemical potentials at zero
temperature. The phase diagram to ${\cal O}(p^2)$ in the $\mu_I$--$\mu_S$ plane
is mapped out with and without electromagnetic effects. The phase diagram
consists of a vacuum phase and three Bose-condensed phases with condensates of
$\pi^{\pm}$, $K^{\pm}$, and $K^{0}/\bar{K}^0$, respectively. Including
electromagnetic interactions, the Bose-condensed phases become Higgs phases via
the Higgs mechanism. The tree-level spectrum for the mesons and gauge bosons is
also derived. We calculate the pressure, energy density, isospin density, and
speed of sound in the pion-condensed phase to ${\cal O}(p^4)$ for three-flavor
$\chi$PT. The results are compared with recent lattice simulations and the
agreement is very good for isospin chemical potentials up to approximately 200
MeV. Moreover, by integrating out the $s$-quark, we show that the thermodynamic
quantities can be mapped onto their two-flavor counterparts with renormalized
parameters. %to ${\cal O}(p^6)$ for two-flavor $\chi$PT in the chiral limit. We
also consider the nonrelativistic limit. It is shown that the energy density
can be matched onto the classic result by Lee, Huang and Yang (LHY) for a
dilute Bose, with an $s$-wave scattering length that includes radiative
corrections. The breaking of the $U(1)$ symmetry in the Bose-condensed phases
gives rise to a Goldstone bosons, whose dispersion is linear for momenta
$p\ll\mu_I$. In this regime, we use Son's prescription to construct an
effective theory for the Goldstone field which is valid in this regime. It is
shown that its damping rate is of order $p^5$. This result is in agreement with
Beliav's for a dilute Bose gas.
