This paper presents a survey on practical as well as theoretical advancements in fractal image compression (FIC) practice. It is a lossy compression scheme comprises Affine Contractive Transforms, Iterated Functions represented as fractals. It is with a high compression ratio, but entails more time for encoding. Although many schemes are published to speed up encoding, they do not easily satisfy the encoding time or the reconstructed image quality requirements. FIC method incorporating optimization techniques results in better performance of the practical applications.