During the last three decades, Bayesian methods have developed greatlyin the field of epidemiology. Their main challenge focusses aroundcomputation, but the advent of Markov Chain Monte Carlo methods (MCMC)and in particular of the WinBUGS software has opened the doors ofBayesian modelling to the wide research community. However modelcomplexity and database dimension still remain a constraint.Recentlythe use of Gaussian random fields has become increasingly popularin epidemiology as very often epidemiological data are characterisedby a spatial and/or temporal structure which needs to be taken intoaccount in the inferential process. The Integrated Nested LaplaceApproximation (INLA) approach has been developed as a computationallyefficient alternative to MCMC and the availability of an R package(R-INLA) allows researchers to easily apply this method.In this paperwe review the INLA approach and present some applications on spatialand spatio-temporal data. © 2012 Elsevier Ltd.