The alternative feedstock, biomass (particularly lignocelluloses), having the profuse availability, is promising for the synthesis of several value-added chemicals which are currently obtained from fossil feedstock. In this article, the synthesis of two extremely significant furan chemicals viz. furfural and 5-hydroxymethylfurfural (HMF) are discussed. In the synthesis of furans from biomass, numerous challenges, i.e., use of edible sugars as substrates, selectivity to furans, their isolation in pure form, reuse of catalyst, environmental issues, etc., are perceived and in the recent past researchers tried to resolve those by developing advance methodologies. This article comprehensively summarizes the latest progress made in the above-mentioned areas and also provides commentary on the analyses of results, rationale for observed activity and mechanisms, etc. It also discusses future aspects of this work.