A geometrization program is an attempt to find systematized divisions of a manifold into parts, each of which can then support an optimal geometry of known type. Both the division and the "optimal" geometry will depend on manifold invariants, so as an additional benefit, a geometrization procedure would show that all manifold invariants are known. Such a program faces considerable difficulty in dimension greater than 3, but there is hope of success if attention is restricted to certain subclasses of manifolds. In this talk, meant for a broad geometry audience, we will investigate the manner in which this is being done for K\"ahler manifolds, what progress has been made, and what can be hoped for in the near future.