Viruses still pose a significant threat to human and animal health worldwide. In the fight against viral infections, high-purity viral stocks are needed for manufacture of safer vaccines. It is also a priority to ensure the viral safety of biopharmaceuticals such as blood products. Chromatography techniques are widely implemented at both academic and industrial levels in the purification of viral particles, whole viruses and virus-like particles to remove viral contaminants from biopharmaceutical products. This paper focuses on polysaccharide adsorbents, particulate resins and membrane adsorbers, used in virus purification/removal chromatography processes. Different chromatographic modes are surveyed, with particular attention to ion exchange and affinity/pseudo-affinity adsorbents among which commercially available agarose-based resins (Sepharose®) and cellulose-based membrane adsorbers (Sartobind®) occupy a dominant position. Mainly built on the development of new ligands coupled to conventional agarose/cellulose matrices, the development perspectives of polysaccharide-based chromatography media in this antiviral area are stressed in the conclusive part.