  We present the first large-scale radiative transfer simulations of cosmic
reionization, in a simulation volume of (100/h Mpc)^3, while at the same time
capturing the dwarf galaxies which are primarily responsible for reionization.
We achieve this by combining the results from extremely large, cosmological,
N-body simulations with a new, fast and efficient code for 3D radiative
transfer, C^2-Ray. The resulting electron-scattering optical depth is in good
agreement with the first-year WMAP polarization data. We show that reionization
clearly proceeded in an inside-out fashion, with the high-density regions being
ionized earlier, on average, than the voids. Ionization histories of
smaller-size (5 to 10 comoving Mpc) subregions exibit a large scatter about the
mean and do not describe the global reionization history well. The minimum
reliable volume size for such predictions is ~30 Mpc. We derive the
power-spectra of the neutral, ionized and total gas density fields and show
that there is a significant boost of the density fluctuations in both the
neutral and the ionized components relative to the total at arcminute and
larger scales. We find two populations of HII regions according to their size,
numerous, mid-sized (~10 Mpc) regions and a few, rare, very large regions tens
of Mpc in size. We derive the statistical distributions of the ionized fraction
and ionized gas density at various scales and for the first time show that both
distributions are clearly non-Gaussian. (abridged)
