  We study possible astrophysical and dark matter (DM) explanations for the
Fermi gamma-ray haze in the Milky Way halo. As representatives of various DM
models, we consider DM particles annihilating into W+W-, b-bbar, and e+e-. In
the first two cases, the prompt gamma-ray emission from DM annihilations is
significant or even dominant at E > 10 GeV, while inverse Compton scattering
(ICS) from annihilating DM products is insignificant. For the e+e- annihilation
mode, we require a boost factor of order 100 to get significant contribution to
the gamma-ray haze from ICS photons. Possible astrophysical sources of high
energy particles at high latitudes include type Ia supernovae (SNe) and
millisecond pulsars (MSPs). Based on our current understanding of Ia SNe rates,
they do not contribute significantly to gamma-ray flux in the halo of the Milky
Way. As the MSP population in the stellar halo of the Milky Way is not well
constrained, MSPs may be a viable source of gamma-rays at high latitudes
provided that there are ~ 20 000 - 60 000 of MSPs in the Milky Way stellar
halo. In this case, pulsed gamma-ray emission from MSPs can contribute to
gamma-rays around few GeV's while the ICS photons from MSP electrons and
positrons may be significant at all energies in the gamma-ray haze. The
plausibility of such a population of MSPs is discussed. Consistency with the
Wilkinson Microwave Anisotropy Probe (WMAP) microwave haze requires that either
a significant fraction of MSP spin-down energy is converted into e+e- flux or
the DM annihilates predominantly into leptons with a boost factor of order 100.
