  Coming up with Bayesian models for spatial data is easy, but performing
inference with them can be challenging. Writing fast inference code for a
complex spatial model with realistically-sized datasets from scratch is
time-consuming, and if changes are made to the model, there is little guarantee
that the code performs well. The key advantages of R-INLA are the ease with
which complex models can be created and modified, without the need to write
complex code, and the speed at which inference can be done even for spatial
problems with hundreds of thousands of observations.
  R-INLA handles latent Gaussian models, where fixed effects, structured and
unstructured Gaussian random effects are combined linearly in a linear
predictor, and the elements of the linear predictor are observed through one or
more likelihoods. The structured random effects can be both standard areal
model such as the Besag and the BYM models, and geostatistical models from a
subset of the Mat\'ern Gaussian random fields. In this review, we discuss the
large success of spatial modelling with R-INLA and the types of spatial models
that can be fitted, we give an overview of recent developments for areal
models, and we give an overview of the stochastic partial differential equation
(SPDE) approach and some of the ways it can be extended beyond the assumptions
of isotropy and separability. In particular, we describe how slight changes to
the SPDE approach leads to straight-forward approaches for non-stationary
spatial models and non-separable space-time models.
