This paper presents a review of a large number of research studies performed during the last few decades that focused on the investigation of cold season extreme precipitation events (EPEs) in the Mediterranean region (MR). The publications demonstrate the important role of anomalously intense transports of moist air from the tropical and subtropical Atlantic in the occurrence of EPEs in the MR. EPEs in the MR are directly or indirectly connected to narrow bands with a high concentration of moisture in the lower troposphere, i.e., atmospheric rivers, along which a large amount of moisture is transported from the tropics to midlatitudes. Whereas in a significant fraction of the EPEs in the western MR moisture is transported to the MR from the tropical Atlantic, EPEs in the central, and especially the eastern, MR are more often associated with intense tropical moisture transports over North Africa and the Red Sea. The moist air for the EPEs in the latter part of the MR also mainly originates from the tropical Atlantic and Indian oceans, and in many cases it serves as a temporary moisture reservoir for future development. The paper is supplemented by the results of a test for a possible connection between declining Arctic sea ice and the climatology of intense precipitation in the eastern MR. Based on the results of the evaluation supporting those from the earlier climate change analyses and modeling studies, it is concluded that a further anthropogenic global warming may lead a greater risk of higher rainfall totals and therefore larger winter floods in western and central parts of the MR as a consequence of stronger and more numerous Atlantic atmospheric rivers, possibly accompanied by a decline in the number of EPEs in the eastern part of the MR.