Space-time monitoring and prediction of environmental variables requires measurements of the environment. But environmental variables cannot be measured everywhere and all the time. Scientists can only collect a fragment, a sample of the property of interest in space and time, with the objective of using this sample to infer the property at unvisited locations and times. Sampling might be a costly and time consuming affair. Consequently, we need efficient strategies to select an optimal design for mapping. Most studies on sampling design optimization consider the case of predictive mapping using geostatistics. In recent years geostatistical models and associated mapping techniques have advanced, which calls for adaptation of associated sampling designs. The main objective of this thesis is to address the optimal design of four some advances in mapping.