Prediction of pathogen emergence is an important field of research, both in human health and in agronomy. Most studies of pathogen emergence have focused on the ecological or anthropic factors involved rather than on the role of intrinsic pathogen properties. The capacity of pathogens to infect a large set of host species, i.e. to possess a large host range breadth (HRB), is tightly linked to their emergence propensity. Using an extensive plant virus database, we found that four traits related to virus genome or transmission properties were strongly and robustly linked to virus HRB. Broader host ranges were observed for viruses with single-stranded genomes, those with three genome segments and nematode-transmitted viruses. Also, two contrasted groups of seed-transmitted viruses were evidenced. Those with a single-stranded genome had larger HRB than non-seed-transmitted viruses, whereas those with a double-stranded genome (almost exclusively RNA) had an extremely small HRB. From the plant side, the family taxonomic rank appeared as a critical threshold for virus host range, with a highly significant increase in barriers to infection between plant families. Accordingly, the plant–virus infectivity matrix shows a dual structure pattern: a modular pattern mainly due to viruses specialized to infect plants of a given family and a nested pattern due to generalist viruses. These results contribute to a better prediction of virus host jumps and emergence risks.