Astronomy is entering a new era of discovery, coincident with the establishment of new facilities for observation and simulation that will routinely generate petabytes of data. While an increasing reliance on automated data analysis is anticipated, a critical role will remain for visualization-based knowledge discovery. We have investigated scientific visualization applications in astronomy through an examination of the literature published during the last two decades. We identify the two most active fields for progress - visualization of large-N particle data and spectral data cubes - discuss open areas of research, and introduce a mapping between astronomical sources of data and data representations used in general purpose visualization tools. We discuss contributions using high performance computing architectures (e.g: distributed processing and GPUs), collaborative astronomy visualization, the use of workflow systems to store metadata about visualization parameters, and the use of advanced interaction devices. We examine a number of issues that may be limiting the spread of scientific visualization research in astronomy and identify six grand challenges for scientific visualization research in the Petascale Astronomy Era.
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