Telemedicine applications allow the patient and doctor to communicate with each other through network services. Several medical image compression techniques have been suggested by researchers in the past years. This review paper offers a comparison of the algorithms and the performance by analysing three factors that influence the choice of compression algorithm, which are image quality, compression ratio, and compression speed. The results of previous research have shown that there is a need for effective algorithms for medical imaging without data loss, which is why the lossless compression process is used to compress medical records. Lossless compression, however, has minimal compression ratio efficiency. The way to get the optimum compression ratio is by segmentation of the image into region of interest (ROI) and non-ROI zones, where the power and time needed can be minimised due to the smaller scale. Recently, several researchers have been attempting to create hybrid compression algorithms by integrating different compression techniques to increase the efficiency of compression algorithms.