Obtaining information (e.g., position, respiration, and heartbeat rates) on humans located behind opaque and non-metallic obstacles (e.g., walls and wood) has prompted the development of non-invasive remote sensing technologies. Due to its excellent features like high penetration ability, short blind area, fine-range resolution, high environment adoption capabilities, low cost and power consumption, and simple hardware design, impulse radio ultra-wideband (IR-UWB) through-wall radar has become the mainstream primary application radar used for the non-invasive remote sensing. IR-UWB through-wall radar has been developed for nearly 40 years, and various hardware compositions, deployment methods, and signal processing algorithms have been introduced by many scholars. The purpose of these proposed approaches is to obtain human information more accurately and quickly. In this paper, we focus on IR-UWB through-wall radar and introduce the key advances in system design and deployment, human detection theory, and signal processing algorithms, such as human vital sign signal measurement methods and moving human localization. Meanwhile, we discuss the engineering pre-processing methods of IR-UWB through-wall radar. The lasts research progress in the field is also presented. Based on this progress, the conclusions and the development directions of the IR-UWB through-wall radar in the future are also preliminarily forecasted.