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We determine conditions for effective quantum control over internal and external degrees of freedom of polar alkali-metal molecules in optical lattices. We show that a relatively modest laser intensity is needed for strong confinement of polar molecules in a lattice and that decoherence effects are manageable. We propose a tunable dipole-dipole interaction between neighboring molecules in an optical lattice by applying microwave radiation. Moreover, we conclude that even though molecules in their internal structure are more complex than atoms, its complexity can be turned into an advantage such as a large polarizability and tuneable dipole forces to entangle the molecules. This makes a regular array of polar molecules a promising system in which to realize a scalable quantum computer as well as to simulate highly correlated many-body states. Our results are based on accurate {\it ab~initio} relativistic electronic structure calculations of the polar KRb and RbCs molecule combined with(INCOMPLETE ABSTRACT SUBMITTED)