Aquaculture is essential to meet global demands for seafood and marine bioproducts, but, as aquaculture intensifies, pests and diseases often impact production and have sometimes lead to industry collapse. Aquaculture activities also pose environmental biosecurity risks including the potential to spread non-native species or disease and to deplete genetic diversity. There is, therefore, strong and growing recognition of the importance of managing aquaculture biosecurity risks to ensure sustainability of both aquaculture industries and the environment. For many established aquaculture species and industries, biosecurity threats and management strategies are well-defined, but a lack of relevant knowledge can impair biosecurity management for aquaculture of novel species. Seaweed aquaculture is an emerging industry in Australia, and a lack of knowledge about biosecurity threats and management strategies is an impediment to seaweed industry development. To address this knowledge gap, we reviewed biosecurity threats affecting seaweed aquaculture globally, including environmental biosecurity hazards, and relevant management strategies applied in seaweed and other aquaculture industries. Here we will present our findings and outline approaches that can be used to manage biosecurity for emerging aquaculture industries, even where knowledge is lacking.