This paper addresses the problem of activity monitoring through change detection in a time series of multidimensional Synthetic Aperture Radar (SAR) images. Thanks to SAR sensors’ all-weather and all-illumination acquisitions capabilities, this technology has become widely popular in recent decades when it concerns the monitoring of large areas. As a consequence, a plethora of methodologies to process the increasing amount of data has emerged. In order to present a clear picture of available techniques from a practical standpoint, the current paper aims at presenting an overview of statistical-based methodologies which are adapted to the processing of noisy and multidimensional data obtained from the latest generation of sensors. To tackle the various big data challenges, namely the problems of missing data, outliers/corrupted data, hetergenenous data, robust alternatives are studied in the statistics and signal processing community. In peculiar, we investigate the use of advanced robust approaches considering non-Gaussian modeling which appear to be better suited to handle high-resolution heterogeneous images. To illustrate the attractiveness of the different methodologies presented, a comparative study on real high-resolution data has been realized. From this study, it appears that robust methodologies enjoy better detection performance through a complexity trade-off with regards to other non-robust alternatives.