Computed tomography (CT) scans have great medical value since it helps clinicians determine clinical staging and surgical range. In offline storage and remote diagnosis, a significant number of CT scan pictures necessitate a huge quantity of storage space and transmission capacity in the Picture Archiving and Communication System (PACS). As a result, in high-quality MRI images, compression is research-oriented. Present compression techniques for CT-scanned images with an increased compression ratio result in data loss on lesions, which may lead to misdiagnosis; compression approaches for CTscanned images and also MRI images with a low compression ratio do not realize the desired effect. As a result, rapid fractalbased image compression in a variety of areas like DWT, DCT, etc. has been reviewed in this paper and its applications in further domains have been discussed.