The past three years have witnessed the striking discovery of twisted multilayer graphene as a versatile plateform to realize quantum phases of matter in a controlled setting. Recent experiments have demonstrated tunable superconductivity, correlated insulators and topological phases. These phases emerge from flat bands in Moire twisted profiles and can be explored at low electrical doping. As our understanding of these graphene systems is improving with an intense theoretical and experimental activity, there are still many open questions on the nature of the exotic phases and on how they can be probed experimentally. The aim of our project is to combine progresses in analyzing the rich physics of twisted graphene materials with a more precise understanding of the various experimental probes to distinguish competing phases, detect superconducting order, insulating mechanisms, topological properties or transport regimes.