New antiviral drugs and new preventive antiviral strategies are a target of intense scientific interest. Thanks to their peculiar properties, nanomaterials play an important role in this field, and, in particular, among metallic materials, silver nanoparticles were demonstrated to be effective against a wide range of viruses, in addition to having a strong antibacterial effect. Although the mechanism of antiviral action is not completely clarified, silver nanoparticles can directly act on viruses, and on their first steps of interaction with the host cell, depending on several factors, such as size, shape, functionalization and concentration. This review provides an overview of the antiviral properties of silver nanoparticles, along with their demonstrated mechanisms of action and factors mainly influencing their properties. In addition, the fields of potential application are analyzed, demonstrating the versatility of silver nanoparticles, which can be involved in several devices and applications, including biomedical applications, considering both human and animal health, environmental applications, such as air filtration and water treatment, and for food and textile industry purposes. For each application, the study level of the device is indicated, if it is either a laboratory study or a commercial product.