  This article gives a comprehensive review on thick brane solutions and
related topics. Such models have attracted much attention from many aspects
since the birth of the brane world scenario. In many works, it has been usually
assumed that a brane is an infinitely thin object; however in more general
situations, one can no longer assume this. It is also widely considered that
more fundamental theories such as string theory would have a minimal length
scale. Many multidimensional field theories coupled to gravitation have exact
solutions of gravitating topological defects, which can represent our brane
world. The inclusion of brane thickness can realize a variety of possible brane
world models. Given our understanding, the known solutions can be classified
into topologically non-trivial solutions and trivial ones. The former class
contains solutions of a single scalar (domain walls), multi-scalar, gauge-Higgs
(vortices), Weyl gravity and so on. As an example of the latter class, we
consider solutions of two interacting scalar fields. Approaches to obtain
cosmological equations in the thick brane world are reviewed. Solutions with
spatially extended branes (S-branes) and those with an extra time-like
direction are also discussed.
