The search for novel topological states of matter, where the quantum phase is characterized not by an order parameter but by some underlying topology, has been the focus of extensive studies since the discovery of the quantum Hall effects in two-dimensional semiconductors. From these studies, a unified understanding on the topological nature of weakly-correlated band insulators has emerged. In this talk, I consider the topological states in strongly correlated systems. Two systems will be discussed: (1) Kondo insulators (heavy fermion topological insulators) and (2) fractional Chern insulator from topological flat bands. For the former, although Kondo insulators are strongly-correlated systems, their topological properties show no fundamental difference from weakly-correlated topological band insulators. In contrast, the latter is an example in which strong correlations result in new topological states beyond topological band insulators.
 Maxim Dzero, Kai Sun, Victor Galitski, and Piers Coleman, Topological Kondo Insulators, Phys. Rev, Lett. 104, 106408 (2010).
 Kai Sun, Zhengcheng Gu, Hosho Katsura and S. Das Sarma, Phys. Rev. Lett. 106, 236803 (2011).
 Ying-Hai Wu, J. K. Jain and Kai Sun, Adiabatic Continuity Between Hofstadter and Chern Insulators, arXiv:1207.4439 (2012)