Traditional work in knowledge representation (KR) aimed to create practical reasoning systems by designing new representations languages and specialized inference algorithms. In recent years, however, an alternative approach based on compiling combinatorial reasoning problems into a common propositional form, and then applying general, highly-efficient search engines has shown dramatic progress. Some domains can be compiled to a tractable form, so that run-time problem-solving can be performed in worst-case polynomial time. But there are limits to tractable compilation techniques, so in other domains one must compile instead to a minimal combinatorial ”core”. The talk will describe how both problem specifications and control knowledge can be compiled together and then solved by new randomized search and inference algorithms.