Radar technology has been utilized for through-the-wall operation in recent years. Through-the-wall radars have become an area of interest due to their usefulness in surveillance, search and rescue operations, and others. We address the specific challenges that through-the-wall radars endure, and present simulations and experimental data for through-the-wall micro-Doppler signatures. The design considerations, including wall attenuation, frequency selection, and dispersion are discussed. Some commonly used time-frequency transforms are briefly discussed with a focus on how they can be used to analyze micro-Doppler signatures. Some of the effects that a barrier such as a wall has on the return microDoppler signals and discusses how these differ from that of micro-Doppler signals that arise without any barrier are demonstrated. Some experimental data of micro-Doppler signatures for targets with and without a translational motion are presented. Some models of common human activities and motions are also discussed and compared to the experimentally measured through-the-wall micro-Doppler signals.