  The kinetic Sunyaev-Zel'dovich (kSZ) effect results from Thomson scattering
by coherent flows in the reionized intergalactic medium. We present new results
based on ray-tracing a 10 Gpc scale simulation at 2-3 Mpc scale resolution to
create a full sky kSZ map. The simulation includes, self-consistently, the
effects of reionization on scales corresponding to multipoles
$10\lesssim\ell\lesssim{5000}$. We separate the kSZ map into Doppler
($\mathbf{v}$), Ostriker-Vishniac ($\delta\mathbf{v}$), patchy ($x\mathbf{v}$),
and third-order ($x\delta\mathbf{v}$) components, and compute explicitly all
the auto and cross correlations (e.g., $\langle\mathbf{v}\mathbf{v}\rangle$,
$\langle\delta\mathbf{v}{x}\mathbf{v}\rangle$, etc.) that contribute to the
total power. We find a complex dependence on the duration of reionization at
$\ell\sim{300}$ and evidence for a non-negligible (10-30 per cent) contribution
from connected four point ionization-velocity correlations,
$\langle{x}\mathbf{v}x\mathbf{v}\rangle_c$, that are usually neglected in
analytical models. We also investigate the Doppler-large scale structure (LSS)
correlation, focusing on two different probes: (1) cross power spectra with
linearly biased tracers of LSS and (2) cold spots from infall onto large, rare
\ion{H}{2} regions centered on peaks in the matter distribution at redshifts
$z>10$. Finally, the reionization history can be reconstructed at 5-10$\sigma$
significance by correlating 21-cm maps with existing CMB temperature maps at
$\ell\!<\!500$ --sophisticated velocity reconstruction methods can probe the
distribution of electrons in the IGM by using combined CMB and LSS measurements
well into the epoch of reionization. The resulting kSZ maps have been made
publicly available at http://www.cita.utoronto.ca/~malvarez/research/ksz-data.
