  We present an analytic model for the sizes of voids in the galaxy
distribution. Peebles and others have recently emphasized the possibility that
the observed characteristics of voids may point to a problem in galaxy
formation models, but testing these claims has been difficult without any clear
predictions for their properties. In order to address such questions, we build
a model to describe the distribution of galaxy underdensities. Our model is
based on the "excursion set formalism," the same technique used to predict the
dark matter halo mass function. We find that, because of bias, galaxy voids are
typically significantly larger than dark matter voids and should fill most of
the universe. We show that voids selected from catalogs of luminous galaxies
should be larger than those selected from faint galaxies: the characteristic
radii range from ~5-10h^{-1} Mpc for galaxies with absolute r-band magnitudes
M_r-5 log(h) < -16 to -20. These are reasonably close to, though somewhat
smaller than, the observed sizes. The discrepancy may result from the void
selection algorithm or from their internal structure. We also compute the halo
populations inside voids. We expect small haloes (M<10^{11} Msun) to be up to a
factor of two less underdense than the haloes of normal galaxies. Within large
voids, the mass function is nearly independent of the size of the underdensity,
but finite-size effects play a significant role in small voids (R<7h^{-1} Mpc).
