Fractal compression of deep space and satellite-derived images using iterated function theory makes it possible to compress these complex natural images into a codified template, from which a facsimile of the original image can be regenerated. The coding technique makes use of the fractal properties of mathematical scale invariance and self-similarity to generate a set of transforms which occupy a minimum amount of space. The result is that these images can be compressed to a fraction of their original size, allowing high compression ratios to be obtained. Image compression using fractal techniques is information lossy. This means that the image generated from the template will be an approximation to the original image. For this reason, raw data should not be processed by such techniques. However, for information retrieval systems, where it is necessary to store many hundreds of images, this technique will allow the capacity of such systems to be increased several fold. This paper will give a brief review of fractals and then describe their use in image compression. The mathematics of iterated function schemes is considered. The coding and decoding schemes utilized in the compression and decompression, respectively, are presented. The paper will finish by showing the results of compression and decompression and will quantify differences between the original and facsimile.