Recent advances in the development of modern satellite sensors have increased the need for image coding, because of the huge volume of such collected data. It is well-known that the Karhunen-Loe^ve transform provides the best spectral decorrelation. However, it entails some drawbacks like high computational cost, high memory requirements, its lack of component scalability, and its difficult practical implementation. In this contributed chapter we revise some of the recent proposals that have been published to mitigate some of these drawbacks, in particular, those proposals based on a divide-and-conquer decorrelation strategy. In addition, we provide a comparison among the coding performance, the compu- tational cost, and the component scalability of these different strategies, for lossy, for progressive lossy-to-lossless, and for lossless remote-sensing image coding.