We review some aspects of the current state of data-intensive astronomy, its methods, and some outstanding data analysis challenges. Astronomy is at the forefront of big data science, with exponentially growing data volumes and data rates, and an ever-increasing complexity, now entering the Petascale regime. Telescopes and observatories from both ground and space, covering a full range of wavelengths, feed the data via processing pipelines into dedicated archives, where they can be accessed for scientific analysis. Most of the large archives are connected through the Virtual Observatory framework, that provides interoperability standards and services, and effectively constitutes a global data grid of astronomy. Making discoveries in this overabundance of data requires applications of novel, machine learning tools. We describe some of the recent examples of such applications.
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