Fractal block coding is a relatively new scheme for image compression. In this dissertation, several ádvanced schemes are proposed based upon Jacquin’s fractal block coding scheme. Exploiting self-similarity at different target block size levels is proposed which allows the self-similarity in the image to be exploited further. Smoother areas are coded with bigger target block sizes while fíne details are coded with smaller target block sizes. More image parts coded at a higher coding level will result in a lower bit rate. Removal of affine-block-wise self-similarity is proposed which includes block-wise self-similarity as a special case. With the utilisation of affineblock-wise self-similarity, the library is substantially enriched which results in a higher probability of coding a target block at a higher coding level. A very fast multi-level fractal block coding scheme exploiting affine-block-wise selfsimilarities is proposed. In the fast coding scheme, self-similarity in the very local area of the target block to be coded is exploited. By using affine-block-wise self-similarity, local correlations are exploited to a much further extent. The number of library blocks used for coding a target block is substantially reduced which results in very fast coding scheme. The proposed fast coding scheme outperforms previous implementations of the fractal block coding technique. A hybrid fractal block coding and DCT scheme is proposed which codes a subsampled image using fractal block coding techniques. The fractal codes are used to decode by zooming to the original image size. The DCT technique is introduced to code the residue image. The proposed scheme is better than the pure fractal block coding scheme. The advanced fractal block coding schemes and the hybrid coder for still images are also applied to video compression which also give some promising simulation results.