There has been increasing concern regarding environmental problems arising from the widespread use of petroleum-based plastic materials for packaging. Many efforts have been made to develop sustainable and biodegradable packaging materials to replace plastic products. The current review summarizes recent research progress in developing cellulose packaging materials to replace plastics used for cushioning and barrier packaging functions based on pulp fibers, cellulose nanofibers, and regenerated cellulose films to benefit from their renewability, sustainability and biodegradability. The cushioning packaging materials include molded pulp products and bio-based foams. Advanced cellulose films and paper can be good barriers for oxygen and carbon dioxide gases, as well as for water vapor. Several cellulose fiber-based packaging products have been commercialized in areas that used to be occupied solely by plastic products.