Drinking water production faces many different challenges with one of them being naturally produced cyanobacterial toxins. Since pollutants become more abundant and persistent today, conventional water treatment is often no longer sufficient to provide adequate removal. Among other emerging technologies, advanced oxidation processes (AOPs) have a great potential to appropriately tackle this issue. This review addresses the economic and health risks posed by cyanotoxins and discusses their removal from drinking water by AOPs. The current state of knowledge on AOPs and their application for cyanotoxin degradation is synthesized to provide an overview on available techniques and effects of water quality, toxin- and technique-specific parameters on their degradation efficacy. The different AOPs are compared based on their efficiency and applicability, considering economic, practical and environmental aspects and their potential to generate toxic disinfection byproducts. For future research, more relevant studies to include the degradation of less-explored cyanotoxins, toxin mixtures in actual surface water, assessment of residual toxicity and scale-up are recommended. Since actual surface water most likely contains more than just cyanotoxins, a multi-barrier approach consisting of a series of different physical, biological and chemical-especially oxidative-treatment steps is inevitable to ensure safe and high-quality drinking water.