Compressive sensing (CS), which breaks the classical Nyquist limit and does not require a high sampling rate, can be used to recover a complete signal by using much less information and an optimization strategy. Further, it reduces the calculations required for signal reconstruction, and requires simpler signal collection and processing than other sensing techniques. It can reduce the data rate of high-resolution imaging radar systems and the amount of sampling, storage, and transmission data effectively. In this study, we first describe the basic theory model of CS. Then, we review the latest developments in radar imaging algorithms based on CS, followed by a comprehensive review of CS applications in high resolution radars, including SARs/ISARs, through-the-wall (TTW) radars, MIIMO radars, and ground-penetrating (GP) radars. This review highlights the importance of CS in simplifying radar hardware, overcoming data limitations, and improving the radar imaging performance. Next, an in-depth discussion and analysis of the advantages and disadvantages of CS-based radar imaging are presented. Finally, we highlight some of the challenges and research directions in this field.