Asgard archaea are globally distributed, newly described microbes related to eukaryotes. Despite their importance, Asgard viruses have not been described. Here we characterize seven double-stranded DNA (dsDNA) viral genomes that infected Lokiarchaeota, Helarchaeota, and Thorarchaeota in deep-sea hydrothermal sediments. These viruses code for Caudovirales-like structural proteins, as well as proteins distinct from those described in archaeal viruses. They contain genes common in eukaryotic nucleocytoplasmic large DNA viruses (NCLDVs), and appear to be capable of semi-autonomous genome replication, repair, epigenetic modifications, and transcriptional regulation. Moreover, Helarchaeota viruses may hijack host ubiquitin systems similar to eukaryotic viruses. Recovery of these Asgard viral genomes reveals they contain features of both prokaryotic and eukaryotic viruses, and provides insights into their roles in the ecology and evolution of their hosts.