An occurrence of a classical pattern p in a permutation \pi is a subsequence
of \pi whose letters are in the same relative order (of size) as those in p. In
an occurrence of a generalized pattern, some letters of that subsequence may be
required to be adjacent in the permutation. Subsets of permutations
characterized by the avoidance--or the prescribed number of occurrences--of
generalized patterns exhibit connections to an enormous variety of other
combinatorial structures, some of them apparently deep. We give a short
overview of the state of the art for generalized patterns.Comment: 11 pages. Added a section on asymptotics (Section 8), added more
examples of barred patterns equal to generalized patterns (Section 7) and
made a few other minor additions. To appear in ``Permutation Patterns, St
Andrews 2007'', S.A. Linton, N. Ruskuc, V. Vatter (eds.), LMS Lecture Note
Series, Cambridge University Pres