  The observable universe could be a 1+3-surface (the "brane") embedded in a
1+3+d-dimensional spacetime (the "bulk"), with standard-model particles and
fields trapped on the brane while gravity is free to access the bulk. At least
one of the d extra spatial dimensions could be very large relative to the
Planck scale, which lowers the fundamental gravity scale, possibly even down to
the electroweak (~ TeV) level. This revolutionary picture arises in the
framework of recent developments in M theory. The 1+10-dimensional M theory
encompasses the known 1+9-dimensional superstring theories, and is widely
considered to be a promising potential route to quantum gravity. General
relativity cannot describe gravity at high enough energies and must be replaced
by a quantum gravity theory, picking up significant corrections as the
fundamental energy scale is approached. At low energies, gravity is localized
at the brane and general relativity is recovered, but at high energies gravity
"leaks" into the bulk, behaving in a truly 1+3+d-dimensional way. This
introduces significant changes to gravitational dynamics and perturbations,
with interesting testable implications for high-energy astrophysics, black
holes and cosmology. Brane-world models offer a phenomenological way to test
some of the novel predictions and corrections to general relativity that are
implied by M theory. This review discusses the geometry, dynamics and
perturbations of simple brane-world models for cosmology and astrophysics,
mainly focusing on warped 5-dimensional brane-worlds based on the
Randall-Sundrum models.
