The catalytic transformation of biomass-based furan compounds (furfural and HMF) for the synthesis of organic chemicals is one of the important ways to utilize renewable biomass resources. Among the numerous high-value products, cyclopentanone derivatives are a kind of valuable compound obtained by the hydrogenation rearrangement of furfural and HMF in the aqueous phase of metal–hydrogen catalysis. Following the vast application of cyclopentanone derivatives, this reaction has attracted wide attention since its discovery, and a large number of catalytic systems have been reported to be effective in this transformation. Among them, the design and synthesis of metal catalysts are at the core of the reaction. This review briefly introduces the application of cyclopentanone derivatives, the transformation mechanism, and the pathway of biomass-based furan compounds for the synthesis of cyclopentanone derivatives. The important progress of metal catalysts in the reaction since the first report in 2012 up to now is emphasized, the characteristics and catalytic performance of different metal catalysts are introduced, and the critical role of metal catalysts in the reaction is discussed. Finally, the future development of this transformation process was prospected.