[Objectives] The evolutionary relationship of Felidae has been controversial. As a result, there are highly divergent views on classification of cats at the generic level. The emerging phylogeny using gene or genomic data provides a new viewpoint to understand the evolution of cats. [Methods] This paper reviews the molecular phylogeny of Felidae over recent years, and we deduce the evolutionary history of Felidae in combination twith fossil records. The phylogenies by Johnson et al. (2006) and Li et al. (2016) are used as the core, corroborated by specific fossil records. [Results] Recent molecular phylogenies propose living cats radiated in the Late Miocene and diverged into eight branches. Though the divergent age of these branches largely coincides with fossil evidence, the inferred origination area of some branches is not supported by fossil records. Combing the evidence from these fossil records, we propose that the most living cat lineages are likely originated in Asia except for the Caracal lineage and Leopardus lineage, and living cats experienced at least 30 intercontinental migrations in the process of evolution, far more than those inferred from only molecular phylogeny. [Conclusion] Based on the study of evolutionary history and morphology, we suggest that all the living cats should be classified into Felinae, and subdivided into 15 genera and 40 species.