We highlight here some of works on impurity scattering and on the vortex state in d-wave superconductor. The model with impurity scattering in the unitarity limit describes not only the rapid suppression of the superconducting transition temperature but also concomitant generation of the residual density of states when Cu in the Cu-O2 plane is substituted by a small amount of Zn. In a magnetic field parallel to the c axis we predict a square vortex lattice tilted by 45”from the α axis is most stable except in the immediate vicinity of T = Tc. The tilted square lattice, though elongated in the b direction, has been seen by small angle neutron scattering experiment and STM imaging in monocrystals of YBCO recently