Abstract: Most modern spatial datasets are very large, often involving tens of thousands to millions of spatial locations. Spatial analysis usually focuses on kriging, i.e., spatial smoothing, which operationally requires inversion of a dense and unstructured covariance matrix whose dimension can be upwards of millions. We introduce an approach to kriging in the presence of large datasets called equivalent kriging, which relies on approximating the kriging weight function using an equivalent kernel. Resulting kriging calculations are extremely fast and feasible in the presence of massive spatial datasets. No likelihood assumptions are required apart from existence of first and second moments, and estimation can proceed by cross validation. We derive explicit kriging approximations for multiresolution classes of spatial processes, as well as under common stationary models such as the Matern. Equivalent kriging will be illustrated on synthetic and real datasets that are otherwise impossible to krige using standard techniques.