**
In this talk, I will review the recent progress on time-reversal
invariant topological insulators in two and three dimensions. In two
dimensions, the time-reversal invariant topological insulator is known
as quantum spin Hall insulators, which has a bulk gap and robust gapless
edge states protected by time-reversal symmetry. The quantum spin Hall
insulator is theoretically predicted to realize in two semiconductor
quantum wells: type-III quantum well HgTe/CdTe and broken-gap type-II
quantum well InAs/GaSb. The prediction in the first material has soon
been confirmed experimentally. As a consequence of the nontrivial
topology, we have shown that a magnetic domain wall on quantum spin Hall
edge traps a half electron charge. Soon after its discovery, the three
dimensional generalization of quantum spin Hall insulator is proposed
theoretically. Two classes of materials are proposed as candidates of
three dimensional topological insulators: BixSb1-x alloy and Bi2Se3,
Bi2Te3, Sb2Te3. Experimental evidences of surface states have been
observed for both classes. We show that the three dimensional
topological insulators are characterized by the topological
magneto-electric effect, corresponding to an ExB term in the free
energy. Due to this effect, the surface of a three-d topological
insulator acts as a "magic mirror", from which the image of an electron
is a magnetic monopole. An electron associated with its image monopole
realizes the composite particle "dyon" proposed in high energy physics
and has fractional statistics.
**

**
**