van der Waals heterostructures are an emergent class of metamaterials that consist of vertically stacked two-dimensional building blocks, which provide us with a vast tool set to engineer their properties on top of the already rich tunability of two-dimensional materials.1 One of the knobs, the twist angle between different layers, has a crucial role in the ultimate electronic properties of a van der Waals heterostructure and does not have a direct analogue in other systems such as MBE-grown semiconductor heterostructures. For small twist angles, the moiré pattern that is produced by the lattice misorientation creates a long-range modulation. So far, the study of the effect of twist angles in van der Waals heterostructures has been mostly concentrated in graphene/hexagonal boron nitride twisted structures, which exhibit relatively weak interlayer interaction owing to the presence of a large bandgap in hexagonal boron nitride.2–5 Here we show experimentally that when two graphene sheets are twisted by an angle close to the theoretically predicted ‘magic angle’ the resulting band structure near charge neutrality becomes flat owing to the strong interlayer coupling.6 These flat bands exhibit insulating phases at half-filling, which are not expected in a non-interacting picture. We show that the half-filling states are consistent with a Mott-like insulator state that can arise from electrons localized in the moiré superlattice. These unique properties of magic-angle twisted bilayer graphene may open a new playground for exotic many-body quantum phases in a two-dimensional platform without magnetic field. The easy accessibility of the flat bands, the electrical tunability, and the bandwidth tunability though twist angle may pave the way towards more exotic correlated systems, such as unconventional superconductors or quantum spin liquids.