This data release contains data and supporting information from a systematic literature review of predictive and forecasting models of Harmful Algal Blooms (HABs) in flowing waters, primarily rivers but also in-stream reservoirs (e.g., run-of-river reservoir and lock-and-dams) and tidal or estuarine environments where unidirectional flow dominates. The systematic literature review began with queries from multiple scientific publication databases, followed by a three-level screening process, and finally information extraction by the authors of this data release. We included only those models that make predictions beyond the calibration datasets in time or space or are utilized for sensitivity or scenario analysis. We excluded purely empirical studies. We required that the modeling effort was motivated by a desire to understand and predict HABs in flowing waters and we did not limit our review to only cyanobacteria or specific modeling endpoints. To extract information from each article, we created a form that each reviewer used when critically reviewing one of the resulting 162 articles. We extracted information about environmental setting, modeling data, model types, and model application. Most questions on the form provided multiple-choice answers or write-in options. The main dataset (review_data.csv) contains information extracted from 162 reviewed articles. Columns in review_data.csv correspond to questions from the form, with additional columns added after critical reviews that include location information (i.e., country and continent), provide aggregated versions of some multiple-choice answers, or harmonize the write-in answers to simplified and standard phrases. The column names are abbreviated character strings for ease of data processing. The additional dataset in this data release, response_definitions.csv, contains the definitions of these column names. Each row in response_definitions.csv describes the responses to a given question on the form, or a description of the extracted information if the question did not use multiple-choice answers.