A typical hierarchical Bayesian spatial modelling framework comprises a three-stage statistical model. In the initial stage, observed areal data are modelled, frequently using normal, Poisson, or binomial distributions. The second stage introduces spatial random effects to account for unexplained variations in the data resulting from unmeasured ecological factors that influence areal differences. In the final stage, we specify the prior distributions for the hyperparameters. To enhance computational efficiency, spatial random effects within this hierarchical structure are frequently modelled using latent Gaussian conditional autoregressive (Gaussian-CAR) distributions. However, the Gaussian assumption may be too restrictive for specific applications. Consequently, employing non-Gaussian spatial random effects can provide significant advantages. This chapter examines robust spatial models for smoothing small-area disease rates by integrating non-Gaussian spatial random effects derived from Laplace and skew-t distributions, known for their long-tailed behaviours. We illustrate the effectiveness of these proposed spatial models by analysing HIV-related indicators in South Africa and comparing our findings to those obtained using the commonly employed Gaussian spatial prior formulation.