The effect of an admixture of spin-polarized fermions to the ground-state properties of ultra-cold bosons in 1D lattice
potentials is discussed. In the two limits of (i) nearly immobile and (ii) very fast fermions a comprehensive understanding of the boson properties can be achieved from effective models. The first case can be mapped to a Bose-Hubbard model with binary disorder, the second to a model with fermion mediated long-range oscillatory interactions between bosons. Corresponding phase diagrams are derived, analyzed and analytic predictions are compared to numerical DMRG simulations. Finally extentions of the standard Bose-Fermi Hubbard model resulting from nonlinear tunnel terms and coupling to higher Bloch bands are discussed.