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With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial datasets observed on large, heterogeneous spatial domains. Many statistical approaches to this problem rely on low-rank models, for which the process of interest is modeled as a linear combination of spatial basis functions plus a fine-scale-variation term. I describe how these low-rank models can be used for the analysis of global data, spatio-temporal data, and distributed data. For an extension of spatial low-rank models that includes a tapered (localized) fine-scale component, I discuss how to make inference on the number, locations, and shapes of the basis functions.