This document reviews different techniques for fractal image compression to enhance compression ratio while maintaining image quality. It discusses algorithms like quadtree partitioning with Huffman coding (QPHC), discrete cosine transform based fractal image compression (DCT-FIC), discrete wavelet transform based fractal image compression (DWTFIC), and Grover's quantum search algorithm based fractal image compression (QAFIC). The document also analyzes works applying these techniques and concludes that combining QAFIC with the tiny block size processing algorithm may further improve compression ratio with minimal quality loss.