Graph isomorphism (GI) is one of the few remaining problems in NP
whose complexity status couldn't be solved by classifying it as
being either NP-complete or solvable in P. Nevertheless, efficient
(polynomial-time or even NC) algorithms for restricted versions of
GI have been found over the last four decades. Depending on the
graph class, the design and analysis of algorithms for GI use tools
from various fields, such as combinatorics, algebra and logic.
In this paper, we collect several complexity results on graph
isomorphism testing and related algorithmic problems for restricted
graph classes from the literature. Further, we provide some new
complexity bounds (as well as easier proofs of some known results)
and highlight some open questions.