  This paper surveys some combinatorial aspects of Smith normal form, and more
generally, diagonal form. The discussion includes general algebraic properties
and interpretations of Smith normal form, critical groups of graphs, and Smith
normal form of random integer matrices. We then give some examples of Smith
normal form and diagonal form arising from (1) symmetric functions, (2) a
result of Carlitz, Roselle, and Scoville, and (3) the Varchenko matrix of a
hyperplane arrangement.
