Because of their ability to operate without regard to day, night or weather conditions, radar systems are ubiquitous in remote sensing operations and are used in a wide variety of commercial and military applications. High resolution radar imaging, however, is a remote sensing subcategory that requires raw radar data to be collected over an artificially extended aperture that is much larger than the radar receiving antenna and processed to create a reflectivity image of a scene (typically by backprojection methods). These synthetic aperture radar imaging (SAR) methods have been in use for over 50 years and, while the methodology for simple radar imaging is quite mature, there are still many active research programs seeking to extend the quality of-and information obtained from-SAR images.At its heart, basic SAR imaging relies on a simplified model in which the electromagnetic waves propagate through vacuum from a known antenna location, and elements of the scene to be imaged are weakly scattering point-like elements whose relative positions are fixed during the data collection interval. When this model fails to accurately represent a particular imaging scenario, the usual result is image artifacts which confound follow-on interpretation. In the case of dynamic scenes, for example, we typically find that the locations of moving scene elements are often significantly displaced in the final image (relative to other scene components). This problem has been recognized for many decades but only recently have concerted research efforts been mounted to attack the issue.Limitations associated with the point scatterer model are not quite so apparent as in the moving target case. Here, the problem is more one of lost information than artifacts (though associated image artifacts are possible as well). Generally, the echo response from a target will be characterized by more than just its intensity and more careful models have lately included depolarization effects and frequency dependence in an effort to more completely characterize the behavior of the reconstructed SAR image.As with any computed image method there will, of course, be issues of effective and efficient algorithm design. Owing to the practical problems of collecting the radar data over a synthetic aperture (often measured by aircraft negotiating imprecise flight paths), the problem of SAR image reconstruction can be especially troublesome. Data registration errors, nonuniform sampling issues and wave propagation through complex media can adversely affect the reliability of the data by adding unknown phase errors which, in turn, reduce image resolution.In this special section, we have invited contributions from many of the leading researchers in the mathematics, physics and engineering of SAR imaging techniques. The papers collected here fall (roughly) into three categories.