Our knowledge of archaeal viruses has increased rapidly over the past four decades since the discovery of the archaeal domain. Most surprising has been the morphological diversity of crenarchaeal viruses that generate several forms not previously observed in the viral sphere. Much recent work has focussed on host-virus interactions and especially on the influence on viral replication of the CRISPR-Cas immune systems that are highly complex in many archaea. Here we provide an overview of archaeal virus biology and summarise many of the major findings on archaeal viruses and their cellular interactions, with a special focus on two model viruses, the rudivirus SIRV2 and the bicaudavirus SMV1. Moreover, we explore insights into the interplay between the host CRISPR-Cas systems and viruses infected singly or in pairs. The evolutionary relationships between archaeal viruses and bacteriophages are also considered.