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 will discuss symmetry breaking, collective modes and detection issues, e.g. in Bragg scattering. On the other hand, 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 role of disorder in optical lattices. Fermionic atoms experience Anderson localization at sufficiently strong disorder. Interactions among the atoms induce a competing tendency towards delocalization. We will present a complete phase diagram obtained within dynamical mean-field theory and discuss experimental observability of the Mott and Anderson phases.