In recent years, green energy sources have been proposed as alternatives for fossil fuels to meet energy demand while minimizing environmental pollution and global climate change. In this context, agricultural residues can be catalytically converted into furan derivatives. Among furan-based compounds, 5-hydroxymethylfurfural (HMF) and 2,5-dimethylfuran (DMF) are the valuable chemicals that can be converted into desired materials, including fuels. This review article discusses various catalytic HMF and DMF production pathways and the influence of feedstocks, catalysts, solvents, and hydrogen donors on the process yield. Additionally, reaction temperature and H2 pressure effects on the feedstock conversion and HMF and DMF production yields are also presented. The primary attention has been devoted to the literature published in the last five years. However, additional relevant examples have also been discussed to clarify the topic further where necessary. This review aims at providing state-to-the-art information on the current developmental state of DMF and HMF production for researchers in this field.