  We present new VLA C+D-array HI observations and optical and NIR imaging of
the well known interacting system NGC 4038/9, ``The Antennae''. The radio data
reveal a wealth of gaseous sub-structure both within the main bodies of the
galaxies and along the tidal tails. In agreement with previous HI studies, we
find that the northern tail has HI along its outer length, but none along its
base. We suggest that the HI at the base of this tail has been ionized by
massive stars in the disk of NGC 4038. The gas in the southern tail has a
bifurcated structure, with one filament lying along the optical tail and
another running parallel to it but with no optical counterpart. The two
filaments join just before the location of several star forming regions near
the end of the tail. The HI velocity field at the end of the tail is dominated
by strong velocity gradients which suggest that at this location the tail is
bending away from us. We delineate and examine two regions within the tail
previously identified as possible sites of a so-called ``tidal dwarf galaxy''
condensing out of the expanding tidal material. The tail velocity gradients
mask any clear kinematic signature of a self-gravitating condensation in this
region. A dynamical analysis suggest that there is not enough mass in gas alone
for either of these regions to be self-gravitating. Conversely, if they are
bound they require a significant contribution to their dynamical mass from
evolved stars or dark matter. (Abridged)
