Cold atoms in optical lattices offer a new laboratory for quantum many-body phenomena.  One of their main advantages is the tunability of interactions and quantum statistics. In this talk I will focus on current developments in multiflavor Fermi gases:
i) We investigate antiferromagnetic ordering of trapped spin-1/2 fermions using large-scale dynamical mean-field theory simulations.  We find a clear experimental signature - enhanced double occupancy - for the onset of magnetic order at low temperatures in current experiments.
ii) We study the properties of three-flavor fermions in an optical lattice, where new exotic quantum states such as color superfluids arise in partial analogy to Quantum Chromodynamics.  Low-temperature properties of this system are addressed using DMRG and dynamical mean-field theory.  We find a strong interplay between magnetization and color superfluidity.