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The canonical technique for nonlinear modeling of spatial/point-referenced data is known as kriging in geostatistics, and as Gaussian Process (GP) regression for surrogate modeling and statistical learning. This article reviews many similarities shared between kriging and GPs, but also highlights some important differences. One is that GPs impose a process that can be used to automate kernel/variogram inference, thus removing the human from the loop. The GP framework also suggests a probabilistically valid means of scaling to handle a large corpus of training data, i.e., an alternative to so-called ordinary kriging. Finally, recent GP implementations are tailored to make the most of modern computing architectures such as multi-core workstations and multi-node supercomputers. We argue that such distinctions are important even in classically geostatistical settings. To back that up, we present out-of-sample validation exercises using two, real, large-scale borehole data sets involved in the mining of gold and other minerals. We pit classic kriging against the modern GPs in several variations and conclude that the latter can more economical (fewer human and compute resources), more accurate and offer better uncertainty quantification. We go on to show how the fully generative modeling apparatus provided by GPs can gracefully accommodate left-censoring of small measurements, as commonly occurs in mining data and other borehole assays.