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We present a state-of-the-art report on visualization in astrophysics. We survey representative papers from both astrophysics and visualization and provide a taxonomy of existing approaches based on data analysis tasks. The approaches are classified based on five categories: data wrangling, data exploration, feature identification, object reconstruction, as well as education and outreach. Our unique contribution is to combine the diverse viewpoints from both astronomers and visualization experts to identify challenges and opportunities for visualization in astrophysics. The main goal is to provide a reference point to bring modern data analysis and visualization techniques to the rich datasets in astrophysics., Funding Agencies|Carnegie Institution for Science Venture [BPO-700082]; Canadian Institute for Advanced Research Fellowship program; Ahmanson Foundation; NASANational Aeronautics & Space Administration (NASA) [NNX16AB93A]; Swedish e-Science Research Centre; Knut and Alice Wallenberg FoundationKnut & Alice Wallenberg Foundation; Swedish Research CouncilSwedish Research CouncilEuropean Commission [DNR:2015-05462]