Biomass can be used as an alternative feedstock for the production of fuels and valuable chemicals, which can alleviate the current global dependence on fossil resources. One of the biomass-derived molecules, 2,5-furandicarboxylic acid (FDCA), has attracted great interest due to its broad applications in various fields. In particular, it is considered a potential substitute of petrochemical-derived terephthalic acid (PTA), and can be used for the preparation of valuable bio-based polyesters such as polyethylene furanoate (PEF). Therefore, significant attempts have been made for efficient production of FDCA and the catalytic chemical approach for FDCA production, typically from a biomass-derived platform molecule, 5-hydroxymethylfurfural (HMF), over metal catalysts is the focus of great research attention. In this review, we provide a systematic critical overview of recent progress in the use of different metal-based catalysts for the catalytic aerobic oxidation of HMF to FDCA. Catalytic performance and reaction mechanisms are described and discussed to understand the details of this reaction. Special emphasis is also placed on the base-free system, which is a more green process considering the environmental aspect. Finally, conclusions are given and perspectives related to further development of the catalysts are also provided, for the potential production of FDCA on a large scale in an economical and environmentally friendly manner.