  Quantum computers promise to efficiently solve important problems classical
computers never will. However, in order to capitalize on these prospects, a
fully automated quantum software stack needs to be developed. This involves a
multitude of complex tasks from the classical simulation of quantum circuits,
over their compilation to specific devices, to the verification of the circuits
to be executed as well as the obtained results. All of these tasks are highly
non-trivial and necessitate efficient data structures to tackle the inherent
complexity. Starting from rather straight-forward arrays over decision diagrams
(inspired by the design automation community) to tensor networks and the
ZX-calculus, various complementary approaches have been proposed. This work
provides a look "under the hood" of today's tools and showcases how these means
are utilized in them, e.g., for simulation, compilation, and verification of
quantum circuits.
