  We review recent developments in the theory of brane tilings and
four-dimensional N=1 supersymmetric quiver gauge theories. This review consists
of two parts. In part I, we describe foundations of brane tilings, emphasizing
the physical interpretation of brane tilings as fivebrane systems. In part II,
we discuss application of brane tilings to AdS/CFT correspondence and
homological mirror symmetry. More topics, such as orientifold of brane tilings,
phenomenological model building, similarities with BPS solitons in
supersymmetric gauge theories, are also briefly discussed.
  This paper is a revised version of the author's master's thesis submitted to
Department of Physics, Faculty of Science, the University of Tokyo on January
2008, and is based on his several papers: math.AG/0605780, math.AG/0606548,
hep-th/0702049, math.AG/0703267, arXiv:0801.3528 and some works in progress.
