Abstract: Traditionally phases of matter are classified by spontaneous symmetry breaking. The discovery of quantum Hall effect in 1980s led to the concept of topological phases characterized by topological quantum numbers. In the past few years, new topological phases have been theoretically predicted and experimentally observed in band insulators at zero magnetic field. These topological insulators are characterized by topological invariants in the band structure. They have protected gapless surface states with Dirac dispersion. I will describe theory of topological insulators, prediction and observation of these new phases in real materials, and recent experiments on topological surface states. I will end by describing recently observed superconductivity in doped topological insulators and its implication for unconventional pairing in spin-orbital coupled materials.