The demand for higher and higher quality images transmitted quickly over the Internet has led to a strong need to develop better algorithms for the filtering and coding of such images. The introduction of the JPEG2000 compression standard has meant that for the first time the discrete wavelet transform (DWT) is to be used for the decomposition and reconstruction of images together with an efficient coding scheme. The use of wavelets implies the use of subband coding in which the image is iteratively decomposed into high- and low-frequency bands. Thus there is a need for filter pairs at both the analysis and synthesis stages. This paper aims in tutorial form to introduce the DWT, to illustrate its link with filters and filterbanks and to illustrate how it may be used as part of an image coding algorithm. It concludes with a look at the qualitative differences between images coded using JPEG2000 and those coded using the existing JPEG standard.