CurviLinear SAR (CLSAR) is increasingly attracting considerable interest in the field of radar remote sensing. Various methods of 3-D target feature extraction and aperture design have been proposed, and these methods are classified in this paper. The basic theories of these methods are systematically studied and compared, and their advantages and disadvantages are summarized. Moreover, the main 3-D target feature extraction and aperture methods are described. Finally, the future research fields of CLSAR are proposed.