Lensless digital holographic imaging could support high resolution, large field of view and three-dimensional (3D) imaging, but improving the resolution and quality of the reconstruction is still challenging. In this review paper, the compressive holographic models based on diffraction propagation method are introduced. Compressive sensing are developed based on total variation regularization and two-step iterative shrinkage/thresholding algorithm. The physical mechanism of removing two-order noise and twin image is discussed. A filter layer is designed to improve the signal to noise ratio of 3D reconstruction. A block-wise algorithm based on effective anti-aliasing region is proposed, which can improve computational efficiency of compressive holography. A single-shot compressive holographic model based on two-angle illumination beam is proposed. It effectively improves the axial resolution of 3D imaging. High-resolution 3D reconstruction of multilayer masks and particle flow field are demonstrated by using this algorithm.