Geostatistical design and analysis methods are increasingly used in disease mapping, particularly in resource-limited settings where uniformly precise mapping may be unrealistically costly and the priority is often to identify critical areas where interventions can have the most health impact. In this thesis, which is based on four papers, we address the problem of geostatistical sampling design. In the first paper, we consider the problem of sampling design for efficient spatial prediction taking account of uncertain covariance structure, in the context of nonadaptive designs. We propose two classes of designs, namely: simple inhibitory and inhibitory plus close pairs. We evaluate the performance of these designs using an average prediction variance criterion and show how the findings are applied to the design of a rolling Malaria Indicator Survey (rMIS) in an ongoing large-scale, five-year malaria transmission reduction project in Malawi. In the second paper, we address the problem of efficient spatial prediction in the context of adaptive geostatistical designs (AGD). We propose two classes of designs based on singleton and batch sampling. We show how our findings inform an AGD of rMIS, in the perimeter of Majete Wildlife Reserve (MWR) in Chikwawa, southern Malawi. The third paper is a commentary on a paper by Ferreira and Gamerman (2015), which addressed the effect of preferential sampling of the locations at which to measure a spatial process. In the fourth paper, we present the first epidemiological field application of AGD sampling in a malaria prevalence survey. We give an in-depth description of the project, the study area and practical implementation of our adaptive sampling strategy. We present prevalence maps for children 6–59 months in MWR perimeter, showing high malaria transmission areas, often called “hotspots”, that could be targeted with interventions.