Aquaculture is the fastest-growing sector worldwide, contributing significant quantities to the supply of food for human consumption and have surpassed wild-capture amounts. The expansion and intensification of aquaculture models from inland to mariculture cause eutrophication, which is often accompanied by algal blooms because of aquatic nutrient loadings (mainly N:P ratio). Harmful algal blooms (HABs) are typically phytoplankton species including Chaetoceros spp., Heterosigma spp., Microcystis spp., Karenia spp., Alexandrium spp., Pyrodinium sp., Noctiluca sp., Dinophys sp., Trichodesmium sp., Prorocentrum sp., Pseudonitzhia sp., and Cochlodinium sp., that produce no or few toxins harmful to wild and farmed fish, shrimp, shellfish, and even humans, causing severe illnesses referred to as paralytic, diarrheic, and amnesic shellfish poisoning in humans who use them. This paper discusses the occurrence of HABs, the factors that generate and maintain HABs, and the negative impacts of HABs on aquaculture in the past, present, and future with the aim of improving the assessment of food poisoning risks to consumers.