Dipolar gases offer a wealth of novel physics compared to non-dipolar ones due to the long-range anisotropic character of the dipole-dipole interaction. Polar molecules in optical lattices are particularly interesting, since the dipolar interactions lead to significant inter-site interactions, which are basically absent in non-dipolar systems. In this talk I will focus on polar molecules in 1D optical lattices. I will first comment on the case of polar bosons at unit filling, which may be mapped to a large extent into a 1D spin-1 chain. I will address in particular the role of disorder and quasi-disorder, with a particular emphasis on the effects of disorder on the Haldane-insulator phase. In the second part of the talk I will discuss the case of polar Fermi molecules in two hyperfine states loaded in zig-zag lattices, showing that they may be employed to simulate spin-orbital Kugel-Khomskii models of interest in solid-state compounds.
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