Even though, in itself, classical simulation of quantum circuits is inherently limited, trying to push it further can yield mathematical tools which are then useful in other contexts, like compilation or optimization of quantum resources. Instances include the stabilizer formalism, decision diagrams (QMDDs) or tensor networks. After quickly reviewing these techniques, we will focus on the simulation of quantum circuits by tensor network contraction. In this case, the quantum circuit itself is seen as a tensor network, and its contraction complexity depends on its underlying graph structure. This technique therefore constitutes an invitation to study the structure of quantum circuits, seen as graphs.