Parasites are very diverse and common in both natural populations and in stocks kept in aquacultural facilities. For most cultured species, there are important bacteria and viruses causing diseases, but eukaryotic parasites are also very important. We review the various combinations of aquacultured species and eukaryotic parasitic groups and discuss other problems associated with aquaculture such as eutrophication, zoonotic species, and invasive species, and we conclude that further development of aquaculture in a sustainable manner must include a holistic approach (One Health) where many factors (e.g., human health, food safety, animal health and welfare, environmental and biodiversity protection and marketability mechanisms, etc.) are considered.