  We describe a general technique that allows to induce and control strong
interaction between spin states of neighboring atoms in an optical lattice. We
show that the properties of spin exchange interactions, such as magnitude,
sign, and anisotropy can be designed by adjusting the optical potentials. We
illustrate how this technique can be used to efficiently ``engineer'' quantum
spin systems with desired properties, for specific examples ranging from
scalable quantum computation to probing a model with non-trivial topological
orders that supports exotic non-abelian anyonic excitations.
