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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-Nordstrom 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-l)-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.