In this paper, we set out general principles and develop geostatistical methods for the analysis of data from spatio‐temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram‐based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood‐based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions of the standard model for disease prevalence that can be used when stationarity of the spatio‐temporal covariance function is not supported by the data. We discuss how to define predictive targets and argue that exceedance probabilities provide one of the most effective ways to convey uncertainty in prevalence estimates. We describe statistical software for the visualisation of spatio‐temporal predictive summaries of prevalence through interactive animations. Finally, we illustrate an application to historical malaria prevalence data from 1 334 surveys conducted in Senegal between 1905 and 2014.