Electromagnetic imaging has been a powerful technique in various civil and military applications across medical imaging, geophysics, and space exploration. The Nyquist-Shannon theory has formed the basis for processing the signals in such systems. The advent of Compressive Sensing techniques has enabled low-dimension-model-based techniques to be used to break many of the bottlenecks of the earlier technologies. Low-dimensional-model-based electromagnetic imaging remains at its early stage, and many important issues relevant to practical applications need to be carefully investigated. In particular, this is the era of big data with booming electromagnetic sensing, by which massive data are being collected for retrieving very detailed information of probed objects. This monograph gives an overview of the low-dimensional models of structure signals, along with its relevant theories and low-complexity algorithms of signal recovery. It further reviews the recent advancements of low-dimensional-model-based electromagnetic imaging in various applied areas. It is a comprehensive introduction for researchers and engineers wishing to understand the state-of-the-art of electromagnetic imaging.