Infections caused by protozoan parasites burden the world with huge costs in terms of human and animal health. Most parasitic diseases caused by protozoans are neglected, particularly those associated with poverty and tropical countries, but the paucity of drug treatments and vaccines combined with increasing problems of drug resistance are becoming major concerns for their control and eradication. In this climate, the discovery/repurposing of new drugs and increasing effort in vaccine development should be supplemented with an exploration of new alternative/synergic treatment strategies. Viruses, either native or engineered, have been employed successfully as highly effective and selective therapeutic approaches to treat cancer (oncolytic viruses) and antibiotic-resistant bacterial diseases (phage therapy). Increasing evidence is accumulating that many protozoan, but also helminth, parasites harbour a range of different classes of viruses that are mostly absent from humans. Although some of these viruses appear to have no effect on their parasite hosts, others either have a clear direct negative impact on the parasite or may, in fact, contribute to the virulence of parasites for humans. This review will focus mainly on the viruses identified in protozoan parasites that are of medical importance. Inspired and informed by the experience gained from the application of oncolytic virus- and phage-therapy, rationally-driven strategies to employ these viruses successfully against parasitic diseases will be presented and discussed in the light of the current knowledge of the virus biology and the complex interplay between the viruses, the parasite hosts and the human host. We also highlight knowledge gaps that should be addressed to advance the potential of virotherapy against parasitic diseases.