  We discuss the prospects for next generation neutrino telescopes, such as
IceCube, to measure the flavor ratios of high-energy astrophysical neutrinos.
The expected flavor ratios at the sources are
$\phi_{\nu_e}:\phi_{\nu_{\mu}}:\phi_{\nu_{\tau}} = 1:2:0$, and neutrino
oscillations quickly transform these to $1:1:1$. The flavor ratios can be
deduced from the relative rates of showers ($\nu_e$ charged-current, most
$\nu_\tau$ charged-current, and all flavors neutral-current), muon tracks
($\nu_\mu$ charged-current only), and tau lepton lollipops and double-bangs
($\nu_\tau$ charged-current only). The peak sensitivities for these
interactions are at different neutrino energies, but the flavor ratios can be
reliably connected by a reasonable measurement of the spectrum shape.
Measurement of the astrophysical neutrino flavor ratios tests the assumed
production mechanism and also provides a very long baseline test of a number of
exotic scenarios, including neutrino decay, CPT violation, and small-$\delta
m^2$ oscillations to sterile neutrinos.
