In a seminal paper on concepts in pedodiversity McBratney (1992) encouraged soil scientists to rethink their approach to soil variability. Historically variation of the soil has been regarded as a problem, the soil scientist wishes to estimate soil properties at some site or region to aid the landmanager. The variations of the soil at multiple spatial scales make this a difficult task, which requires substantial sampling effort and sophisticated statistical methods. McBratney proposed that this variation is actually a positive benefit, and hypothesized that "the maintenance of soil variability is necessary for sustainable soil management." This is a hypothesis, not a dogma, and requires testing. McBratney proposed that the geostatistical methods, by then well established as tools for mapping soil variation by Best Linear Unbiased Prediction (BLUP) from sample data may offer a framework for the quantitative assessment of soil variation, and so for the testing of hypotheses about pedodiversity. The contention of this paper is that the geostatistical model of spatial variation may be too restrictive when our primary interest is in understanding variation, rather than in estimating properties in the presence of variation. In particular geostatistics requires the assumption of statistical stationarity; that is the variables under study are assumed to be a realization of a stochastic process of uniform variance. This is not a realistic model of the spatial variation of soil properties. Their variation may change from one part of a landscape to another, and characterizing this heterogeneity, and its scale dependence is essential for the study of pedodiversity. In this paper I discuss how the wavelet transform can be used to model scale dependent and non-stationary variation in the soil. This technique, and the insights that it can give, have appeared in the soil science literature (e.g. Lark & Webster, 1999; Redding et al., 2003; Lark et al., 2004), but are still to be fully taken up and applied in the study of pedodiversity. I shall consider two types of problem. One is the study of functional pedodiversity (McBratney, 1992) where the spatial variation of a soil process and the soil and landscape features that it reflects is the focus of interest. Here the example is the emission of trace gases from the soil in an agricultural landscape. This is an important area since increased emissions of greenhouse gases (such as nitrous oxide and ammonia) may result from efforts to sustain pedodiversity by increasing carbon sequestration in certain environments. The second problem is the characterization of what McBratney (1992) called taxonomic pedodiversity. The spatial distribution of soil classes is complex with components at different spatial scale. In some case studies I shall show how wavelet analysis can be used to identify such complexity (so identifying where the taxonomic pedodiversity changes at some scale of generalization) and to identify the spatial scales and locations in a landscape at which the taxonomic pedodiversity is reflected by the functional pedodiversity of the soil. References: (i) Lark R.M. & Webster R. 1999. Analysis and elucidation of soil variation using wavelets. European Journal of Soil Science. 50, 185–206. (ii) Lark, R.M., Milne, A.E., Addiscott, T.M., Goulding, K.W.T., Webster, C.P. & O'Flaherty, S. 2004. Scale- and location-dependent correlation of nitrous oxide emissions with soil properties: an analysis using wavelets. European Journal of Soil Science. 55, 601–610. (iii) Redding T.E., Hope G.D., Fortin M.J., Schmidt M.G. & Bailey W.G. 2003. Spatial patterns of soil temperature and moisture across subalpine forest-clearcut edges in the southern interior of British Columbia. Canadian Journal of Soil Science. 83, 121–130. (iv) McBratney, A.B. 1992. On variation, uncertainty and informatics in environmental soil management. Australian Journal of Soil Research. 30, 913–935.