Several sulfated seaweed polysaccharides show high antiviral activity against enveloped viruses, including important human patogens such as human immunodeficiency virus, herpes simplex virus, human citomegalovirus, dengue virus and respiratory syncytial virus. They can be obtained in major amounts and at low costs, have low toxicity and in some cases, lack anticoagulant effects. Even if the systemic applications have many drawbacks, their structure and mode of action indicate potential for topical uses to prevent virus infection. The herpes simplex viruses attach to cells by an interaction between the envelope glycoprotein C and the cell surface heparan sulfate (HS). The virus-cell complex is formed by ionic interactions between the anionic (mainly sulfate) groups in the polysaccharide and basic amino acids of the glycoprotein, and non-ionic ones depending on hydrophobic amino acids interspersed between the basic ones in the glycoprotein-binding zone. Hypothesis are advanced of the corresponding hydrophobic structures in the polysaccharides. The antiviral activity of the sulfated seaweed polysaccharides is based on the formation of formally similar complexes that block the interaction of the viruses with the cells. Correlations are established between different structural parameters and antiviral activity. The minimal, ionic and hydrophobic, structures in the seaweed polysaccharides were hypothesized by comparison of the polysaccharides with the known minimal binding structure in HS / heparin, together with a correlation between those structures of the polysaccharides and their antiviral activity.