We present a comprehensive review of multivariate geostatistical models, focusing on the bivariate case. We compare in detail three approaches, the linear model of coregionalisation, the common component model and the kernel convolution approach, and discuss similarities between them. We demonstrate the merits of the common component class of models as a flexible means for modelling bivariate geostatistical data of the type that frequently arises in environmental applications. In particular, we show how kernel convolution can be used to approximate the common component model, and demonstrate the method using a data-set of calcium and magnesium concentrations in soil samples. We then apply the model to a study of domestic radon concentrations in the city of Winnipeg, Canada, in which exposure was measured at two sites (bedroom and basement) in each residential location. Our analysis demonstrates that in this study the correlation between the two sites within each house dominates the short-range spatial correlation typical of the distribution of radon.