Image compression has many applications. For example, it is an important step for distributed and network based pattern recognition. For real time object recognition or reconstruction, image compression can greatly reduce the image size, and hence increase the processing speed and enhance performance. Fractal image compression is a relatively recent image compression method. Its basic idea is to represent images as a fixed point of a contractive Iterated Function System (IFS). Spiral Architecture (SA) is a novel image structure on which images are displayed as a collection of hexagonal pixels. The efficiency and accuracy of image processing on SA have been demonstrated in many recently published papers. We have shown the existence of contractive IFS's through the construction of a Complete Metric Space on SA. The selection of range and domain blocks for fractal image compression is highly related to the uniform image separation specific to SA. In this paper, we will review the current research work on fractal image compression based on SA. We will compare the results obtained on SA and the traditional square structure in terms of compression ratio and PSNR.