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.