Chitin is one of the most abundant biopolymers on Earth but under-utilized. The effective conversion of chitin biomass to useful chemicals is a promising strategy to make full use of chitin. Among chitin-derived compounds, some furan derivatives, typically 5-hydroxymethylfurfural and 3-acetamido-5-acetylfuran, have shown great potential as platform compounds in future industries. In this review, different catalytic systems for the synthesis of nitrogen-free 5-hydroxymethylfurfural and nitrogen-containing 3-acetamido-5-acetylfuran from chitin or its derivatives are summarized comparatively. Some efficient technologies for enhancing chitin biomass conversion have been introduced. Last but not least, future challenges are discussed to enable the production of valuable compounds from chitin biomass via greener processes.