Multimedia involves a myriad of data and multidimensional signals, including not only plain and formatted text, but also mathematical and other symbols, tables, vector and bitmap graphics, images, sound, animation, video, and interactive virtual reality objects. Space or airborne remote sensing also produces very large images. Telemedicine and telerobotics require signal monitoring and multichannel video transmission. Compression of such signals is usually necessary to fit them into the available communications channels and digital storage, or for data mining. This paper provides an overview of important compression methods and techniques, including lossless entropy coding techniques designed to reduce the redundancy in the critical multimedia material, as well as lossy coding techniques designed to preserve the relevancy of the noncritical multimedia material. Modern lossy techniques often employ wavelets, wavelet packets, fractals, and neural networks. Progressive image transmission is also employed to deliver the material quickly. The paper also addresses several approaches to blind separation of signal from noise (denoising) to improve the compression, and to the difficult question of objective and subjective image quality assessment through complexity metrics.