Studies investigating associations between health outcomes and exposure to environmental pollutants benefit from measures of exposure made at the individual level. In this thesis we consider geostatistical modelling strategies aimed at providing such individual-level estimates. We present three papers showing how to adapt the standard univariate stationary Gaussian geostatistical model according to the nature of the exposure under consideration. In the first paper, we show how informative spatio-temporal covariates can be used to simplify the correlation structure of the assumed Gaussian process. We apply the method to data from a historical cohort study in Newcastle-upon-Tyne, designed to investigate links between adverse birth outcomes and maternal exposure to black smoke, measured by a fixed network of monitoring stations throughout a 32-year period. In the second paper, we show how predictions in the stationary Gaussian model change when the data and prediction locations cannot be measured precisely, and are therefore subject to positional error. We demonstrate that ignoring positional error results in biased predictions with misleading prediction errors. In the third paper, we consider models for multivariate exposures, concentrating on the bivariate case. We review and compare existing modelling strategies for bivariate geostatistical data and fit a common component model to a data-set of radon measurements from a case-control study designed to investigate associations with lung cancer in Winnipeg, Canada.