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This article focuses on recent progress in physical compressive sampling under the Defense Advanced Research Agency's Analog-to-Information (A-to-I) and Multiple Optical Non-Redundant Aperture Generalized Sensors (MONTAGE) programs. A-to-I and MONTAGE focus on aggressive forms of generalized sampling under which measurements consist of transformations, projections, or encodings of the signal onto discrete digital data. The central system design challenge is to select features, sampling strategies and hardware that enable high fidelity signal estimation from these features. The A-to-I and MONTAGE projects differ in application and implementation A-to-I seeks to revolutionize very high temporal bandwidth analog to digital signal conversion whereas MONTAGE seeks to revolutionize very high spatial bandwidth analog to digital signal conversion.