Through-the-Wall Radar Imaging (TWRI) is an emerging technology which enables us to detect behind the wall targets using electromagnetic signals. TWRI has received considerable attention recently due to its diverse applications. This paper presents fundamentals, mathematical foundations and emerging applications of TWRI with special emphasis on Compressive Sensing (CS) and sparse image reconstruction.Multipath propagation stemming from the surrounding walls and nearby targets are among the impinging challenges.Multipath components produce replicas of the genuine target, ghosts, during image reconstruction which may significantly increase the probability of false alarm. The resulting ghost not only creates confusion with genuine targets but may deteriorate the performance of (CS) algorithms as described in this article. The results from a practical scenario show a promising future of the technology which can be adopted in real-life problems including rescue missions and military purposes