In through-the-wall radar imaging (TWRI), the presence of front and side walls causes multipath propagation, which creates fake targets called multipath ghosts. They populate the scene and reduce the probability of correct target detection, classification, and localization. In modern TWRI, specular multipath exploitation has received considerable attention for reducing the effects of multipath ghosts. However, this exploitation is challenged by the requirements of the reflecting geometry, which is not always available. Currently, the demand for a high radar image resolution dictates the use of a large aperture and wide bandwidth. This results in a large amount of data. To tackle this problem, compressive sensing (CS) is applied to TWRI. With CS, only a fraction of the data are used to produce a high-quality image, provided that the scene is sparse. However, owing to multipath ghosts, the scene sparsity is highly deteriorated; hence, the performance of the CS algorithms is compromised. This paper presents and discusses the adverse effects of multipath ghosts in TWRI. It describes the physical formation of ghosts, their challenges, and existing suppression techniques.This work was supported by the National Plan for Science, Technology and Innovation (Maarifah) of the Science and Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia (15-ELE4651-04, Multipath Exploitation in Through the Wall Radar Imaging with UWB Sparse Signals).