Illegal excavations in archaeological heritage sites (namely "looting") are a global phenomenon. Satellite images are nowadays massively used by archaeologists to systematically document sites affected by looting. In parallel, remote sensing scientists are increasingly developing processing methods with a certain degree of automation to quantify looting using satellite imagery. To capture the state-of-the-art of this growing field of remote sensing, in this work 47 peer-reviewed research publications and grey literature are reviewed, accounting for: (i) the type of satellite data used, i.e., optical and synthetic aperture radar (SAR); (ii) properties of looting features utilized as proxies for damage assessment (e.g., shape, morphology, spectral signature); (iii) image processing workflows; and (iv) rationale for validation. Several scholars studied looting even prior to the conflicts recently affecting the Middle East and North Africa (MENA) region. Regardless of the method used for looting feature identification (either visual/manual, or with the aid of image processing), they preferred very high resolution (VHR) optical imagery, mainly black-and-white panchromatic, or pansharpened multispectral, whereas SAR is being used more recently by specialist image analysts only. Yet the full potential of VHR and high resolution (HR) multispectral information in optical imagery is to be exploited, with limited research studies testing spectral indices. To fill this gap, a range of looted sites across the MENA region are presented in this work, i.e., Lisht, Dashur, and Abusir el Malik (Egypt), and Tell Qarqur, Tell Jifar, Sergiopolis, Apamea, Dura Europos, and Tell Hizareen (Syria). The aim is to highlight: (i) the complementarity of HR multispectral data and VHR SAR with VHR optical imagery, (ii) usefulness of spectral profiles in the visible and near-infrared bands, and (iii) applicability of methods for multi-temporal change detection. Satellite data used for the demonstration include: HR multispectral imagery from the Copernicus Sentinel-2 constellation, VHR X-band SAR data from the COSMO-SkyMed mission, VHR panchromatic and multispectral WorldView-2 imagery, and further VHR optical data acquired by GeoEye-1, IKONOS-2, QuickBird-2, and WorldView-3, available through Google Earth. Commonalities between the different image processing methods are examined, alongside a critical discussion about automation in looting assessment, current lack of common practices in image processing, achievements in managing the uncertainty in looting feature interpretation, and current needs for more dissemination and user uptake. Directions toward sharing and harmonization of methodologies are outlined, and some proposals are made with regard to the aspects that the community working with satellite images should consider, in order to define best practices of satellite-based looting assessment. [ABSTRACT FROM AUTHOR]