The paper discusses the principles behind the R-INLA software package, which provides an interface for continuous domain spatial models using the integrated nested Laplace approximation (INLA) method. INLA is a computationally efficient alternative to Markov Chain Monte Carlo (MCMC) for Bayesian inference, particularly suitable for latent Gaussian models. The package supports stationary and non-stationary spatial models, as well as spatio-temporal models, and is applicable in various fields such as epidemiology, ecology, and environmental risk assessment. The authors describe how SPDEs (stochastic partial differential equations) can be used to express a wide class of random field models, including those with Matérn covariance functions. This approach allows for the approximation of continuous domain spatial models using Gaussian Markov random field (GMRF) representations, which are computationally efficient and allow for local parameter specification. The paper also covers the implementation details of the R-INLA interface, including mesh construction, mapping between meshes and continuous space, SPDE model construction, and plotting. It emphasizes the importance of abstracting the underlying bookkeeping to simplify the user experience, making it easier to work with continuous domain models in a discrete setting. Finally, the paper provides an example of how to use SPDE models in latent Gaussian models for direct Bayesian inference using the INLA method, demonstrating the practical application of the software package.The paper discusses the principles behind the R-INLA software package, which provides an interface for continuous domain spatial models using the integrated nested Laplace approximation (INLA) method. INLA is a computationally efficient alternative to Markov Chain Monte Carlo (MCMC) for Bayesian inference, particularly suitable for latent Gaussian models. The package supports stationary and non-stationary spatial models, as well as spatio-temporal models, and is applicable in various fields such as epidemiology, ecology, and environmental risk assessment. The authors describe how SPDEs (stochastic partial differential equations) can be used to express a wide class of random field models, including those with Matérn covariance functions. This approach allows for the approximation of continuous domain spatial models using Gaussian Markov random field (GMRF) representations, which are computationally efficient and allow for local parameter specification. The paper also covers the implementation details of the R-INLA interface, including mesh construction, mapping between meshes and continuous space, SPDE model construction, and plotting. It emphasizes the importance of abstracting the underlying bookkeeping to simplify the user experience, making it easier to work with continuous domain models in a discrete setting. Finally, the paper provides an example of how to use SPDE models in latent Gaussian models for direct Bayesian inference using the INLA method, demonstrating the practical application of the software package.