Aquaculture is the fastest food-producing sector in the world, accounting for one-third of global food production. As is the case with all intensive farming systems, increase in infectious diseases has adversely impacted the growth of marine fish farming worldwide. Viral diseases cause high economic losses in marine aquaculture. We provide an overview of the major challenges limiting the control and prevention of viral diseases in marine fish farming, as well as highlight potential solutions. The major challenges include increase in the number of emerging viral diseases, wild reservoirs, migratory species, anthropogenic activities, limitations in diagnostic tools and expertise, transportation of virus contaminated ballast water, and international trade. The proposed solutions to these problems include developing biosecurity policies at global and national levels, implementation of biosecurity measures, vaccine development, use of antiviral drugs and probiotics to combat viral infections, selective breeding of disease-resistant fish, use of improved diagnostic tools, disease surveillance, as well as promoting the use of good husbandry and management practices. A multifaceted approach combining several control strategies would provide more effective long-lasting solutions to reduction in viral infections in marine aquaculture than using a single disease control approach like vaccination alone.