We describe a model-based approach to analyse space–time count data. Such data can arise as a number of time series of counts, each representing a specific geographical area, i.e. as spatial time series, or as a number of spatial maps at different time points, i.e. as temporal spatial processes. We propose a Bayesian hierarchical formulation capable of embracing both cases, with principal kriging functions combined with latent parameters having prior distributions able to deal with spatial/temporal dependence. The methodology is applied to monitoring problems in environmental and epidemiological applications. Copyright © 2010 John Wiley & Sons, Ltd.