The application relates to processes and systems that use a furfural compound for producing five-membered carbocyclic rings that are unsaturated, such as cyclopentene and cyclopentadiene. Examples methods for conversion of furfural compounds may include converting a furfural compound to at least a five-membered, saturated carbocyclic ring, and converting the five-membered, saturated carbocyclic ring in a presence of a catalyst to at least a five-membered, unsaturated carbocyclic ring.