In today’s digital world, data transmission and storage is becoming a massive problem. This is because the data produced by various sensors worldwide is outstripping the ability to store them. Pre-processing the entire data before transmission is the best solution for reducing the storage issue. ‘Compressed sensing’(CS) is a pre-processing technique that exploits the sparsity of the signal for sampling the data. Since most of the natural signals are sparse, CS allows sampling at a rate lesser than that required in Nyquist sampling theorem. However, in conventional CS, sampling is done for the entire image at once which increases processing time and reduces visual quality. In block compressed sensing (BCS), blocks of the images are processed simultaneously which increases processing speed and decreases the processing time. To improve the quality of the reconstructed signal, a variant of BCS, Adaptive block compressed sensing (ABCS) is used. This review paper studies the advantages, challenges and applications of applying ABCS for image compression.