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The study of covariances (or positive definite functions) on the sphere (theEarth, in our motivation) goes back to Bochner and Schoenberg (1940--42) and tothe first author (1969, 1973), among others. Extending to the geotemporal case(sphere cross line, for position and time) was for a long time an obstacle togeostatistical modelling. The characterisation question here was raised by theauthors and Mijatovi\'c in 2016, and answered by Berg and Porcu in 2017.Extensions to multiple products (of spheres and lines) follows similarly(Guella, Menegatto and Peron, 2016). We survey results of this type, andrelated applications e.g. in numerical weather prediction.

Probability, Statistics and Planet Earth, I: Geotemporal covariances