The recent development of lattice atom optics is introauced,including atomic optical lattices,atomic magnetic lattices and magneto-optical lattices,and some new results of atomic magnetic lattices and magneto-optical lattices,and some new results on the investigations of magnetic and magneto-optical lattices are reported. Afterwards,some recent progresses of dynamic process of cold atoms and Bose-Einstein-condensed atoms in optical lattices,and coherent propagation and control of quantum states are briefly reviewed. Finally,potential applications of atomic optical lattices,atomic magnetic lattices and magneto-optical lattices in the preparation of photonic crystals and so on are briefly introduced.