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High temperature superconductivity still remains an exciting and challenging subject of research in condensed matter physics. In particular, the so-called pseudogap behavior of underdoped high Tc superconductors below a characteristic temperature may hold the key to the understanding of the mechanism of the superconductivity. Recently, a broken symmetry state called d-density wave has been proposed for an explanation of the pseudogap phase. I will review the general properties of high temperature superconductors, including pseudogap behavior and phase diagram. I will discuss experimental signatures of the d-density wave state, and compare theoretical predictions with recent neutron scattering measurements. Broader implication of these results to strongly correlated electron systems will be also discussed.