Linear transforms are the basis for many techniques used in image processing, image analysis, and image coding. Subband transforms are a subclass of linear transforms which offer useful properties for these applications. In this chapter, we discuss a variety of subband decompositions, compare their properties and illustrate their use in image coding. In particular, we consider the Gabor transform, the block DCT and LOT, the Laplacian pyramid, and 1D and 2D QMF (wavelet) pyramids.