The current interest in biomass derived renewable furan derivatives furfural and 5-hydroxymethylfurfural commonly known as biofurans is due to their ready accessibility through dehydration of abundant cellulosic biomass derived monosaccharides. However, an upgrading to more stable compounds is an essential step for these materials in many sustainable fuel and chemical industry applications due to their instability and facile polymerization to humins. The aim of this article is to cover all aspects of catalytic upgrading reactions of biofurans, especially focusing on the developments in the last five years. The importance of this class of renewable feedstocks, preparation from monosaccharides as well as the diversity of possible transformations are discussed in the introduction sections of this review. The recent advances in catalytic reductions and oxidations of biofurans at CHO, OH functional groups, in ring system as well as rearrangements to form more stable value-added derivatives are reviewed. In addition, recently developed catalytic methods in carbon number upgrading of biofurans through condensation reactions and further conversions to renewable synthetic fuel range molecules are discussed in the article.