Abstract
In this thesis, we study interesting few-body and many-body physics in different polar molecule systems. By loading polar molecules in two tubes and applying a static electric field to polarize dipoles, we can find many exotic few-body complexes when we change the angel between the electric field and the tubes. Further, the interaction between polar molecules can be shaped by applying an external AC field to couple internal states of polar molecules. A new type of bound states (supermolecules) can be formed in this system. We show that the supermolecules are quite long-lived. Moreover, by loading the polar molecules into a deep optical lattice, we can design effective spin models by controlling external electric fields. A mean-field study for XY model with both transverse and longitudinal field is also presented.