In traditional imaging systems, a two-dimensional pixel array detector is usually used to record the object’s image. However, in the scheme of single-pixel imaging, only a bucket detector without spatial resolution capability is needed for signal measurement. Then one can reconstruct the image with different algorithms on a computer. Compared with pixel array detector, the manufacturing cost is relatively low for a bucket detector, so the single-pixel imaging technique attracts a great deal of researchers, especially in the wavebands of X ray, near infrared imaging and terahertz imaging. Moreover, extensive attention of single-pixel imaging has also focused on the applications of fluorescence imaging, multi-spectral imaging, 3D imaging and complex wavefront imaging. Especially in the field of complex wavefront imaging, because it is important to the applications of astronomy, medical diagnosis and optical measurement. Researchers have proposed a large number of single-pixel imaging schemes to measure an unknown complex amplitude field, and these works may help the single-pixel imaging technique be used in different practical scenes. In this review, the development and basic principle of single-pixel imaging technique were introduced. Further, the application of single-pixel imaging in the field of complex amplitude measuring was reviewed and discussed detailly.