Ultracold atoms and Bose-Einstein condensates in optical lattices

For ultracold and Bose-condensed atoms contained in periodic optical potential wells the quantized nature of their motion is clearly visible. The motion of the atomic wavepacket can also be accurately controlled. For those systems the long-range character of the atomic interaction and of the external potential play a key role in the quantum mechanical evolution. The basic facets of the experimental and theoretical research for atoms within optical lattice structures will be reviewed.