Current methods for the design and analysis of neglected tropical disease prevalence surveys largely rely on classical survey sampling ideas that treat prevalence data from different locations as an independent random sample from the probability distribution induced by a random sampling design. We set out an alternative, explicitly geospatial paradigm that can deliver much more precise estimates of the geospatial variation in prevalence over a country or region of interest. We describe the advantages of this approach under three headings: streamlining, whereby more precise results can be obtained with smaller sample sizes; integrating, whereby a joint analysis of data from two or more diseases can bring further gains in precision; and adapting, whereby the choice of future sampling location is informed by past data.