Abstract: Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents stabilizer states. Recently, there has been an effort to unify them and use them to grow the current landscape of simulatable systems. In this talk we present a formalism for universal circuit simulation using these tools, discuss a unifying description of current approaches, and show some of the simulations that have been enhanced so far with it. This research raises interesting questions on the representation power of tensor networks and the properties of quantum resources such as entanglement and magic.