ABSTRACT Three issues related to the inversion of random fields in groundwater flow problems are reviewed: problem formulation, computational methods and application methodology. Regarding the first, we show that most current methods can be viewed as particular cases of minimum variance estimation. While theory suggests that non-linear methods should lead to more accurate estimation and more realistic evaluation of uncertainty, differences obtained in intercomparison exercises appear to be much less significant than expected. This can be partly attributed to the fact that differences are more significant in the case of large variances, in the presence of sink/source terms, for large head data density and for small head measurement errors. Regarding computational aspects we present an improved version of the adjoint state method which should reduce significantly the computational burden of transient geostatistical inversion problems. Finally, application methodology is illustrated with a case comprising abundant steady-state head data and drawdowns from three pumping tests observed at a large set of points.