Cold atoms in optical lattices offer an exciting new laboratory where quantum
many-body phenomena can be realized in a highly controlled way. They can even
serve as quantum simulators for notoriously difficult problems like
high-temperature superconductivity. This review is focussed on recent
developments and new results in multi-component systems. Fermionic atoms with
SU(N) symmetry have exotic superfluid and flavor-ordered ground states. We
discuss symmetry breaking, collective modes and detection issues. Bosonic
multi-flavor ensembles allow for engineering of spin Hamiltonians which are
interesting from a quantum computation point of view. Finally, we will address
the competition of disorder and interaction in optical lattices. We present a
complete phase diagram obtained within dynamical mean-field theory and discuss
experimental observability of the Mott and Anderson phases.Comment: 13 pages, 9 eps figures included, Adv. Solid State Phys. (in press
