I will argue that the driving force for the transition from geochemistry to biochemistry was natural selection operating, in its earliest stages, on inorganic materials. The most critical requirement for truly primitive evolvable systems is truly primitive genetic materials. These should have the kind of permutable structure that can hold information, and they should be able to replicate this information—very accurately for the most part. They should be like DNA in these respects. But, unlike DNA, they must do it all without any pre-evolved systems. Mixed-layer and polytypic materials will be featured in attempts to sketch what we should be looking for.