  This thesis is devoted to studying two important aspects of braneworld
physics: their cosmology and their holography. We examine the Einstein
equations induced on a general $(n-2)$-brane of arbitrary tension, embedded in
some $n$-dimensional bulk. The brane energy-momentum tensor enters these
equations both linearly and quadratically. From the point of view of a
homogeneous and isotropic brane we see quadratic deviations from the FRW
equations of the standard cosmology. There is also a contribution from a bulk
Weyl tensor. We study this in detail when the bulk is AdS-Schwarzschild or
Reissner-Nordstr\"om AdS. This contribution can be understood holographically.
For the AdS-Schwarzschild case, we show that the geometry on a brane near the
AdS boundary is just that of a radiation dominated FRW universe. The radiation
comes from a field theory that is dual to the AdS bulk. We also develop a new
approach which allows us to consider branes that are not near the AdS boundary.
This time the dual field theory contributes quadratic energy density/pressure
terms to the FRW equations. Remarkably, these take exactly the same form as for
additional matter placed on the brane by hand, with no bulk Weyl tensor.
  We also derive the general equations of motion for a braneworld containing a
domain wall. For the critical brane, the induced geometry is identical to that
of a vacuum domain wall in $(n-1)$-dimensional Einstein gravity. We develop the
tools to construct a nested Randall-Sundrum scenario whereby we have a
``critical'' domain wall living on an anti-de Sitter brane. We also show how to
construct instantons on the brane, and calculate the probability of false
vacuum decay.
