  We review recent attempts to address the cosmological constant problem and
the late-time acceleration of the Universe based on braneworld models. In
braneworld models, the way in which the vacuum energy gravitates in the 4D
spacetime is radically different from conventional 4D physics. It is possible
that the vacuum energy on a brane does not curve the 4D spacetime and only
affects the geometry of the extra-dimensions, offering a solution to the
cosmological constant problem. We review the idea of supersymmetric large extra
dimensions that could achieve this and also provide a natural candidate for a
quintessence field. We also review the attempts to explain the late-time
accelerated expansion of the universe from the large-distance modification of
gravity based on the braneworld. We use the Dvali-Gabadadze-Porrati model to
demonstrate how one can distinguish this model from dark energy models in 4D
general relativity. Theoretical difficulties in this approach are also
addressed.
