During their life span, most viruses are both living and non-living organisms. Whether they are living or non-living depends on if they have found a host.
When a virus is without a host, it is considered dormant. When the virus is dormant, no biological activity is taking place, which makes it non-living. A virus without a host is called a "virion." Once the virus finds an appropriate host, however, the biological processes become active and it is considered living. When it has found a host and comes alive, it is then officially a virus. This is the stage in which it replicates.