  During the last decade, many exciting phenomena have been experimentally
observed and theoretically predicted for ultracold atoms in optical lattices.
This paper reviews these rapid developments concentrating mainly on the theory.
Different types of the bosonic systems in homogeneous lattices of different
dimensions as well as in the presence of harmonic traps are considered. An
overview of the theoretical methods used for these investigations as well as of
the obtained results is given. Available experimental techniques are presented
and discussed in connection with theoretical considerations. Eigenstates of the
interacting bosons in homogeneous lattices and in the presence of harmonic
confinement are analysed. Their knowledge is essential for understanding of
quantum phase transitions at zero and finite temperature.
