**Abstract**

The objective of this chapter is to present the methodology of some of the models used in the area of epidemiology, which are used to study, understand, model and predict diseases (infectious and non-infectious) occurring in a given region. These models, which belong to the area of geostatistics, are usually composed of a fixed part and a random part. The fixed part includes the explanatory variables of the model and the random part includes, in addition to the error term, a random term that generally has a multivariate Gaussian distribution. Based on the random effect, the spatial correlation (or covariance) structure of the data will be explained. In this way, the spatial variability of the data in the region of interest is accounted for, thus avoiding that this information is added to the model error term. The chapter begins by introducing Gaussian processes, and then looks at their inclusion in generalized spatial linear models, spatial survival analysis and finally in the generalized extreme value distribution for spatial data. The review also mentions some of the main packages that exist in the R statistical software and that help with the implementation of the mentioned spatial models.

**Keywords:** Geostatistic, gaussian process, spatial GLM, spatial survival analysis, spatial extremes
