Fractal image compression depends on representing an image using affine transformations. The main concern for researches in the discipline of fractal image compression (FIC) algorithm is to decrease encoding time needed to compress image data. The basic technique is that each portion of the image is similar to other portions of the same image. In this process, there are many models that were developed. The presence of fractals was initially noticed and handled using Iterated Function System (IFS); that is used for encoding images. In this paper, a review of fractal image compression is discussed with its variants along with other techniques. A summarized review of contributions is achieved to determine the fulfillment of fractal image compression, specifically for the block indexing methods based on the moment descriptor.  Block indexing method depends on classifying the domain and range blocks using moments to generate an invariant descriptor that reduces the long encoding time. A comparison is performed between the blocked indexing technology and other fractal image techniques to determine the importance of block indexing in saving encoding time and achieving better compression ratio while maintaining image quality on Lena image.