  We discuss a Brane World scenario where we live on a 3-brane with massive
gravity in infinite-volume bulk. The bulk graviton can be much heavier than the
inverse Hubble size, as heavy as the bulk Planck scale, whose lower bound is
roughly the inverse of 0.1 mm. The 4D Einstein-Hilbert term on the brane
shields the brane matter from both strong bulk gravity and large bulk graviton
mass. Gravity on the brane does not become higher-dimensional at large
distances. Instead, at distance scales above the bulk Planck length, gravity on
the brane behaves as 4D gravity with small graviton mass roughly of order or
below the inverse Hubble size. Unlike the massless case, with massive gravity
in the bulk one can have: i) 4D tensor structure on a codimension-1 brane; and
ii) no infrared tachyon for smoothed-out higher codimension branes. The effects
of the brane dynamics on the bulk are exponentially suppressed away from the
brane. One consequence is that there are no "self-accelerated" solutions. In
codimension-2 cases there exist nonsingular solutions with a flat 3-brane for a
continuous positive range of the brane tension. In higher codimension cases, as
in the massless case, higher curvature terms are required to obtain such
solutions.
