The recent successful creation of a high phase-space-density gas of polar 40K 87Rb molecules  has been based on both new experimental and theoretical advances in manipulating and understanding properties of these molecules. There are great expectations for the application of ultracold molecules in simulating many-body states, in quantum information processing, and in performing high-precision measurements. In this talk I will describe our theoretical contribution to the KRb experiment, which influenced the creation of polar molecules in their absolute ro-vibrational ground state. In particular, the succession of laser excitation steps that is needed to produce cold polar molecules, requires precise knowledge of molecular structure and other properties. Our analysis includes a multi-channel bound-state calculation of the hyperfine and Zeeman mixed vibrational levels of the ground state potentials. We find excellent agreement with the hyperfine structure observed in experimental data. Moreover, we studied spin-orbit mixing in the intermediate state of the Raman transition. This allowed us to investigate its effect on the transition dipole moment to the lowest ro-vibrational level of the ground state. In addition, we studied the interplay between the short- and long-range interactions of ultracold molecules, their strength and vibrational dependence. We determined the van der Waals coefficients between molecules from their dynamic polarizability at imaginary frequencies. From this we have found the collisional lifetimes of ultracold molecules based on a quantum approach, which solely relies on the van der Waals coefficient and a few parameters that describe the short-range chemical potential of two molecules. To explore the anisotropic properties of polar molecules we studied rotationless J = 0 polar molecules in the presence of strong DC electric fields as well as the focussed laser beam that traps the molecules. This anisotropy appears due to mixing of the J = 0 level with higher J levels. As a result, the trapping potential changes with polarization of the trapping light. Those analysis are based on a calculation of static and dynamic polarizability. Its knowledge allows us to select laser frequencies, which minimize decoherence from loss of molecules due to spontaneous or laser induced transitions.  K.-K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Peer, B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Julienne, D. S. Jin, and J. Ye, Science 322, 231 (2008).
10 minute talk: Matter Wave Scattering from Cold Aoms in an Optical Lattice