Most of the 25 viruses found in globe artichoke (Cynara scolymus L.) and cardoon (Cynara cardunculus L.) were recorded from Europe and the Mediterranean basin, where they decrease both the productivity and the quality of the crop. Although, sometimes, these viruses are agents of diseases of different severity, most often their infections are symptomless. These conditions have contributed to spread virus-infected material since farmers multiply traditional artichoke types vegetatively with no effective selection of virus-free plants. This review reports the main properties of these viruses and the techniques used for their detection and identification. ELISA kits are commercially available for most of the viruses addressed in this review but have seldom been used for their detection in artichoke. Conversely, nucleic acid-based diagnostic reagents, some of which are commercially available, have successfully been employed to identify some viruses in artichoke sap. Control measures mainly use virus-free stocks for new plantations. A combined procedure of meristem-tip culture and thermotherapy proved useful for producing virus-free regenerants of the reflowering southern Italian cultivar Brindisino, which kept earliness and typical heads shape.