This program will describe some of the Data Compression Groups recent projects: (i) Group testing for image compression is a new flexible technique for achieving high quality lossy image compression and (ii) Unequal loss protection for compressed images and video is a way to obtain graceful degradation of fidelity in the presence of packet loss. It will also describe some of the basic principles in image and video compression including discrete cosine transforms, wavelet transforms, bit plane coding, and motion compensation. To conclude it will then describe several projects that have used group testing or unequal loss protection to achieve their results. From the Series:CSE Colloquia - 2001