Treating a viral disease is no simple feat. Drug resistance, latent reservoirs in the body, emerging novel viruses, and a frequent lack of specific treatments all complicate antiviral therapy. For decades, antiviral polymers have been studied for a range of infectious diseases. The field has emerged, expanded, and adapted over the past 70 years, producing unique classes of materials that hold promise for overcoming these obstacles. Antiviral polymers can directly inhibit viral replication and infection, usually by binding to the virus and preventing it from invading a host cell. They can also serve as microbicides or antiviral drug-delivery vehicles. This Perspective outlines the significant advances and challenges in the field. We discuss polymers with activity against viruses with limited treatment options (hepatitis C), ubiquitous presence (influenza, norovirus), or long-term complications (HIV). We also explore insights into different mechanisms of action, and we offer ideas on how the field of antiviral polymers might advance in the future.