1940–1979
Krige develops spatial interpolation for mine valuation. Whittle discovers the SPDE–Matérn connection. Matheron formalises kriging; Kimeldorf & Wahba show splines are GP posterior means. Cliff & Ord and Besag develop the lattice model tradition independently.
1980–1999
Geman & Geman's Gibbs sampler triggers Bayesian hierarchical spatial modelling. BYM becomes standard for disease mapping. GP regression reaches machine learning via Rasmussen & Williams. Vecchia (1988) introduces the conditional independence approximation that underlies NNGP and MRA.
2000–2011
Rue & Held systematise GMRFs; INLA makes Bayesian inference tractable without MCMC. Lindgren, Rue & Lindström (2011) show Matérn GP ↔ sparse GMRF via SPDE — connecting all three tracks. Scalable GP approximations begin: predictive processes (2008), covariance tapering (2006).
2012–2019
The big-n problem drives a proliferation of scalable methods: LatticeKrig (2015), NNGP (2016), MRA (2017), periodic embedding (2019). Heaton et al. (2019) hold the community competition. MRA wins simulated (RMSE 0.83); SPDE wins satellite (RMSE 1.53). Katzfuss & Guinness (2021) unify many methods under the Vecchia framework.