  Basic properties of cold Bose atoms in optical lattices are reviewed. The
main principles of correct self-consistent description of arbitrary systems
with Bose-Einstein condensate are formulated. Theoretical methods for
describing regular periodic lattices are presented. A special attention is paid
to the discussion of Bose-atom properties in the frame of the boson Hubbard
model. Optical lattices with arbitrary strong disorder, induced by random
potentials, are treated. Possible applications of cold atoms in optical
lattices are discussed, with an emphasis of their usefulness for quantum
information processing and quantum computing. An important feature of the
present review article, distinguishing it from other review works, is that
theoretical fundamentals here are not just mentioned in brief, but are
thoroughly explained. This makes it easy for the reader to follow the principal
points without the immediate necessity of resorting to numerous publications in
the field.
