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Conventional Soil Survey is described briefly and several quantitative methods of improvement proposed in the last decade discussed. Lateral or spatial variability of soil properties still remains a stumbling block to increased precision of spatial prediction. The study attempts to identify methods to overcome this problem. The problem of spatial variability is placed in a stochastic framework allowing variation to be an intrinsic part of the modelling process. Concepts of stationarity and spatial dependence of random functions and regionalised variables are introduced and the semi-variogram is shown to be a useful robust descriptor of continuous spatial variation. The statistical and practical aspects of semi-variogram modelling are discussed in detail and several and varied practical examples given. An alternative approach using ARMA models is briefly discussed. These approaches represent a significant improvement in our ability to model soil variability but some practical problems remain including tests for stationarity and confidence limits for semi-variogram estimates. The problems of spatially predicting soil properties are discussed along with various interpolation methods. Kriging, an optimal spatial predictor, has very desirable properties, especially those of minimum and known predicted estimation variance and the ability to take into account the spatial variation information contained in the semi-variogram. Ordinary point and block kriging are used successfully on several data sets to produce isarithmic maps. Block kriging seems particularly useful. A comparison of the predicted estimation variances of kriging with those of Conventional Soil Survey shows kriging to be much more precise. The techniques of semi-variogram estimation and kriging are extended from single properties to situations where there are two or more spatially interdependent ones. The cross semi-variogram is introduced and models fitted. Co-kriging is described in the context of spatially predicting a variable from measurement of it plus data on one or more spatially cross-correlated properties that have been sampled more intensively. For a real example, co-kriging gives more intricate contour maps and lower estimation variances than kriging, which in turn is more precise than Conventional Soil Survey. Knowledge of the semi-variogram and the cross semi-variogram can be utilised to design optimal sampling schemes, in the sense of maxium precision for a given sampling effort, for estimating the regional mean and for local spatial prediction using kriging and co-kriging. In all cases certain triangular grids are shown to be optimal with certain rectangular grids only slightly less so. The techniques of semi-variogram and cross semi-variogram analysis, kriging and co-kriging, and optimal sampling strategies can be combined into a single methodology called Geostatistical Soil Survey. It is shown that Geostatistical Soil Survey is largely complementary to Conventional Soil Survey because of differences in aim, scale and number of properties examined. There is some overlap however. It is concluded that Geostatistical Soil Survey is most useful for medium to large scale surveys with specific aims and where a few properties provide the required soil information. Furthermore, the firm statistical basis provided by Geostatistical Soil Survey makes it possible to apply with confidence further quantitative methods to improve the value of soil survey operations. Suggestions for further work include testing of the Geostatistical Soil Survey methodology and research into improved geostatistical methods. Finally, the use of geostatistics in the design and analysis of field experiments is discussed briefly.