Recently, a new class of topological states has been theoretically predicted and experimentally observed. The topological insulators have an insulating gap in the bulk, but have topologically protected edge or surface states due to the time reversal symmetry. Similarly, topological superconductors or superfluids have novel edge or surface states consisting of Majorana fermions. In this talk, I shall review the recent theoretical and experimental progress in the field, and focus on a number of outstanding issues, including the quantized anomalous Hall effect, quantized magneto-electric effect, the topological Mott insulators and the search for topological superconductors.

A. Bernevig, T. Hughes and S. C. Zhang, Science, 314, 1757, (2006)
M. Koenig et al, Science 318, 766, (2007)
Xiao-Liang Qi, Taylor Hughes and Shou-Cheng Zhang, Phys. Rev B. 78, 195424 (2008)
Haijun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang, and Shou-Cheng Zhang, Nature Physics 5, 438 (2009).
Xiao-Liang Qi, Run-Dong Li, Jiadong Zang and Shou-Cheng Zhang, Science 323, 1184 (2009).
Xiao-Liang Qi, Taylor L. Hughes, Srinivas Raghu and Shou-Cheng Zhang, Phys. Rev. Lett. 102, 187001 (2009)