Flexible long period moir e superlattices form in two-dimensional van der Waals crystals containing layers that differ slightly in lattice constant or orientation. In this Letter we show theoretically that isolated flat moir e bands described by generalized triangular lattice Hubbard models are present in twisted transition metal dichalcogenide heterobilayers. The hopping and interaction strength parameters of the Hubbard model can be tuned by varying the twist angle and the three-dimensional dielectric environment. When the flat moire bands are partially filled, candidate many-body ground states at some special filling factors include spin-liquid states, quantum anomalous Hall insulators and chiral $d$-wave superconductors.
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