Aquaculture is the fastest growing food sector globally and protein provisioning from aquaculture now exceeds that from wild capture fisheries. There is clear potential for the further expansion of marine aquaculture (mariculture), but there are associated risks. Some naturally occurring algae can proliferate under certain environmental conditions, causing deoxygenation of seawater, or releasing toxic compounds (phycotoxins), which can harm wild and cultured finfish and shellfish, and also human consumers. The impacts of these so-called harmful algal blooms (HABs) amount to approximately 8 $billion/yr globally, due to mass mortalities in finfish, harvesting bans preventing the sale of shellfish that have accumulated unsafe levels of HAB phycotoxins and unavoided human health costs. Here, we provide a critical review and analysis of HAB impacts on mariculture (and wild capture fisheries) and recommend research to identify ways to minimise their impacts to the industry. We examine causal factors for HAB development in inshore versus offshore locations and consider how mariculture itself, in its various forms, may exacerbate or mitigate HAB risk. From a management perspective, there is considerable scope for strategic siting of offshore mariculture and holistic Environmental Approaches for Aquaculture, such as offsetting nutrient outputs from finfish farming, via the co-location of extractive shellfish and macroalgae. Such pre-emptive, ecosystem-based approaches are preferable to reactive physical, chemical or microbiological control measures aiming to remove or neutralise HABs and their phycotxins. To facilitate mariculture expansion and long-term sustainability, it is also essential to evaluate HAB risk in conjunction with climate change.