The compressive sensing (CS) scheme exploits many fewer measurements than suggested by the Nyquist-Shannon sampling theorem to accurately reconstruct images, which has attracted considerable attention in the computational imaging community. While classic image CS schemes employ sparsity using analytical transforms or bases, the learning-based approaches have become increasingly popular in recent years. Such methods can effectively model the structure of image patches by optimizing their sparse representations or learning deep neural networks while preserving the known or modeled sensing process. Beyond exploiting local image properties, advanced CS schemes adopt nonlocal image modeling by extracting similar or highly correlated patches at different locations of an image to form a group to process jointly. More recent learning-based CS schemes apply nonlocal structured sparsity priors using group sparse (and related) representation (GSR) and/or low-rank (LR) modeling, which have demonstrated promising performance in various computational imaging and image processing applications.