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Atomically thin layers of various materials can be combined - almost at will - into novel artificial materials, with graphene structures being the most prominent examples. If two (or more) layers are combined at a certain twist angle between the crystal orientations, an additional periodic modulation of the atomic lattice potential can emerge, often referred to as moiré superlattice. At specific, gate tunable electron fillings, various emergent electronic phases have been identified, most notably superconductivity, ferromagnetism, or Mott insulators, all driven by the Coulomb interaction between the electrons. Similar electronic phases were recently discovered in twisted bilayer structures of atomically thin semiconductors, especially in transitionmetal dichalcogenides (TMDCs), investigated mostly by optical spectroscopy, with the drawback that optical excitations alone are already complicated many-particle states, while low-frequency transport experiments are often not directly related to fundamental properties.