  We present deep ($>$2.4 Ms) observations of the Cassiopeia A supernova
remnant with {\it NuSTAR}, which operates in the 3--79 keV bandpass and is the
first instrument capable of spatially resolving the remnant above 15 keV. We
find that the emission is not entirely dominated by the forward shock nor by a
smooth "bright ring" at the reverse shock. Instead we find that the $>$15 keV
emission is dominated by knots near the center of the remnant and dimmer
filaments near the remnant's outer rim. These regions are fit with unbroken
power-laws in the 15--50 keV bandpass, though the central knots have a steeper
($\Gamma \sim -3.35$) spectrum than the outer filaments ($\Gamma \sim -3.06$).
We argue this difference implies that the central knots are located in the 3-D
interior of the remnant rather than at the outer rim of the remnant and seen in
the center due to projection effects. The morphology of $>$15 keV emission does
not follow that of the radio emission nor that of the low energy ($<$12 keV)
X-rays, leaving the origin of the $>$15 keV emission as an open mystery. Even
at the forward shock front we find less steepening of the spectrum than
expected from an exponentially cut off electron distribution with a single
cutoff energy. Finally, we find that the GeV emission is not associated with
the bright features in the {\it NuSTAR} band while the TeV emission may be,
suggesting that both hadronic and leptonic emission mechanisms may be at work.
