Dimensionality reduction methods have played a central role in exploration of parsimonious structural models, complexity regularization in inverse problems, and data compression. Examples are PCA, Laplacian eigenmaps, ISOMAP, and matching pursuits which attempt to fit a subspace to the data. For integrated sensing and processing (ISP) systems dimensionality reduction must go beyond simply fitting the data geometry. One must account for how dimension reduction will affect the performance of the processing task, e.g., image reconstruction or classification, and sensor scheduling, e.g., path planning or waveform design. We will present some thoughts and recent progress on dimensionality reduction for ISP.