<p>Images are used widely nowadays. Images are used in many fields such as medicine to terrain mapping. There is a need to compress the images and represent them in shorter form for effective transmission. Several techniques are reviewed in this paper. The first group of techniques is the data compression technique. The data compression methods are Huffman encoding, Lempel–Ziv Welch (LZW), arithmetic encoding, run length encoding, and Shannon-Fano encoding. The second group of methods is prediction, here the neighboring pixels are utilized in the prediction of the present pixel and the error is encoded using an entropy encoder. In wavelet-based techniques, the source image is transformed from the spatial domain to the wavelet domain, and the coefficients are encoded. In learning-based techniques, a neural network is used to model the image data for compression. Fractal encoding is a compression method that searches for similar blocks in an image and compresses the difference between the blocks. With an average bitrate of 4.87 bpp (bits per pixel) on the first 10 photos of the Digital Imaging and Communications in Medicine (DICOM) image collection, the results indicate that LZW is the top performing data compression technique among the data compression techniques. In prediction-based techniques, Context Adaptive Lossless Image Codec (CALIC) is the best performing with 3.5 bpp. The modern neural method, compressive autoencoder outperforms established methods such as Joint Photographic Experts Group<b> (</b>JPEG), by achieving a PSNR of 35 on the Kodak dataset compared with 32 PSNR on the same dataset at 1.0 bpp.</p>