  This paper is intended to provide an introduction to the theory of
substitution tilings. For our purposes, tiling substitution rules are divided
into two broad classes: geometric and combinatorial. Geometric substitution
tilings include self-similar tilings such as the well-known Penrose tilings;
for this class there is a substantial body of research in the literature.
Combinatorial substitutions are just beginning to be examined, and some of what
we present here is new. We give numerous examples, mention selected major
results, discuss connections between the two classes of substitutions, include
current research perspectives and questions, and provide an extensive
bibliography. Although the author attempts to fairly represent the as a whole,
the paper is not an exhaustive survey, and she apologizes for any important
omissions.
