It has been established as a result of successful direct experimental studies of the symmetry of the superconducting order parameter that the pairing symmetry in the compounds YBCO, GdBCO, Tl2201, and Bi2212 is of thed-wave type. In this paper, experimental and theoretical results concerning thed-wave superconducting state and the peculiarities of magnetic properties of thed-type superconductor such as pseudogap, charge ordering, and unusual structure of vortex excitations differing from that fors-states are analyzed. Several mechanisms ofd-pairing and related microscopic theories are discussed and possible experiments for their verification are proposed. ©1998 American Institute of Physics.