The sparse microwave imaging combines the sparse signal processing theory with radar imaging to obtain new theory, new system, and new methodology of microwave imaging. In this paper, a brief review of fundamental issues in applying sparse signal processing to radar imaging is provided, including sparse representation, measurement matrix construction, unambiguity reconstruction, and so on. The developments of sparse signal processing in microwave imaging are discussed, and the initial airborne experiments on the prototype Synthetic Aperture Radar (SAR) framework with sparse constraints are introduced. The results demonstrate the feasibility and effectiveness of the principle and methodology of sparse microwave imaging. Besides, we also provide an overview of sparse signal processing in various radar applications, including Tomographic SAR (TomoSAR), Inverse SAR (ISAR), Ground Penetrating Radar (GPR) as well.