We have used data from the Sloan Digital Sky Survey (SDSS) Data Release 5 to explore the overall structure and substructure of the stellar halo of the Milky Way using about 4 million color-selected main sequence turn-off stars. We fit oblate and triaxial broken power-law models to the data, and found a `best-fit oblateness of the stellar halo 0.5<c/a<0.8, and halo stellar masses between Galactocentric radii of 1 and 40kpc of (3.7+/-1.2)x10^8 M_sun. The density profile of the stellar halo is approximately r^{-3}; it is possible that the power law slope is shallower inside 20kpc and steeper outside that radius. Yet, we found that all smooth and symmetric models were very poor fits to the distribution of stellar halo stars because the data exhibit a great deal of spatial substructure. We quantified deviations from a smooth oblate/triaxial model using the RMS of the data around the model profile on scales >~100pc, after accounting for the (known) contribution of Poisson uncertainties. The fractional RMS deviation of the actual stellar distribution from any smooth, parameterized halo model is >~40%: hence, the stellar halo is highly structured. We compared the observations with simulations of galactic stellar halos formed entirely from the accretion of satellites in a cosmological context by analysing the simulations in the same way as the data. While the masses, overall profiles, and degree of substructure in the simulated stellar halos show considerable scatter, the properties and degree of substructure in the Milky Ways halo match well the properties of a `typical stellar halo built exclusively out of the debris from disrupted satellite galaxies. Our results therefore point towards a picture in which an important fraction of the Milky Ways stellar halo has been accreted from satellite galaxies.
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