The exceedance set of a spatial or spatio-temporal process is the set of locations where the response exceeds some threshold of interest. Identification of these regions is particularly important in environmental and health applications, as these regions are frequently the ones most impacted by an environmental event or where there is greatest concern for public health. Recently developed methodology for confidently identifying exceedance regions with known confidence will be presented. Extra care must be taken when applying this method to very large spatial and spatio-temporal data sets. Extended discussion will focus on how this methodology can be extended with flexible spatial models suitable for inference using very large spatial and spatio-temporal data sets. These methods will be applied in assessing the scope of impact for recent unusual climate events in the United States.