In this chapter we detail how to fit separable space-time models. A separable space-time model is defined as a SPDE model for the spatial domain and an autoregressive model of order 1, i.e., AR(1), for the time dimension. The space-time separable model is defined by the Kronecker product between the precision matrices of the spatial and temporal random effects. Additional information about separable space-time models can be found in Cameletti et al. (2013).