A moiré superlattice is formed by two similar lattices but with small lattice mismatch. Recently, exciting experimental results are reported in moiré superlattices of graphene and transition metal dichalcogenide (TMD). In this talk, I would like to discuss our theoretical understanding of such moiré systems. The take-home message is that, compared with atomic lattices, moiré superlattices can be regarded as rescaled solids with similar “chemistry”, but tunable band structure and interaction strength on the energy scale of 10~100 meV. The interplay between such “moiré chemistry” and Coulomb interactions lead to various correlated phases, which may help us to understand graphene [1, 2, 3] and TMD superlattices . If I have time, weak coupling approach in momentum space considering the so-called high-order van Hove singularity [5, 6] will also be discussed.
 N. F. Q. Yuan and L. Fu, Phys. Rev. B 98, 045103 (2018).
 M. Koshino, N. F. Q. Yuan, T. Koretsune, M. Ochi, K. Kuroki, and L. Fu, Phys. Rev. X 8, 031087 (2018).
 H. Isobe, N. F. Q. Yuan, and L. Fu, Phys. Rev. X 8, 041041 (2018).
 Yang Zhang*, Noah F. Q. Yuan*, and Liang Fu, arXiv: 1910.14061 (2019).
 Noah F. Q. Yuan, Hiroki Isobe, Liang Fu, arXiv:1901.05432 (2019), to appear on Nature Communications.
 Noah F. Q. Yuan, Liang Fu, arXiv:1910.10179 (2019).