  Steiner triple systems form one of the most studied classes of combinatorial
designs. Configurations, including subsystems, play a central role in the
investigation of Steiner triple systems. With sporadic instances of small
systems, ad-hoc algorithms for counting or listing configurations are typically
fast enough for practical needs, but with many systems or large systems, the
relevance of computational complexity and algorithms of low complexity is
highlighted. General theoretical results as well as specific practical
algorithms for important configurations are presented.
