Moiré patterns are ubiquitous in layered van der Waals materials and can now be fabricated with considerable control by combining mechanical exfoliation of van der Waals layers with tear and stack device fabrication techniques. I will explain why the electronic and optical properties of two-dimensional semiconductors and semimetals are strongly altered in long-period moiré superlattices, focusing in particular on the remarkable example of twisted bilayer graphene.
When twisted to a magic  relative orientation angle near 1 degree the moiré superlattice minibands of bilayer graphene become extremely narrow and electronic correlations become strong. Experimental studies  of magic-angle twisted bilayer graphene (MATBG) have demonstrated that the electronic ground state can be a superconductor, a metal, or an insulator, depending on the filling of the magic angle flat bands. Insulating states occur close to most integer values of the number of electrons per moiré superlattice period, whereas superconducting states are common at fractional moiré band filling factors. In some cases, the insulating states are purely orbital ferromagnets that exhibit a quantum anomalous Hall effect and have superlattice bands with non-zero topological Chern indices C. I will discuss progress that has been made toward understanding these remarkable properties
 Moire bands in twisted double-layer graphene, R. Bistritzer and A.H. MacDonald, PNAS 108, 12233 (2011).
 Magic-angle graphene superlattices: a new platform for unconventional superconductivity, Y. Cao et al. Nature (2018).