Viral infections are a serious health challenge, and the COVID-19 pandemic has increased the demand for antiviral measures and treatments for clean surfaces, especially in public places. Here, we review a range of natural and synthetic surface materials and coatings with antiviral properties, including metals, polymers and biopolymers, graphene and antimicrobial peptides, and their underpinning antiviral mechanisms. We also discuss the physico-chemical properties of surfaces which influence virus attachment and persistence on surfaces. Finally, an overview is given of the current practices and applications of antiviral and virucidal materials and coatings in consumer products, personal protective equipment, healthcare and public settings. The COVID-19 pandemic has highlighted the importance of materials and coatings for antiviral surfaces. Here, a comprehensive review is performed for natural and synthetic antiviral and virucidal materials, including a discussion of their underpinning mechanisms.