An important problem in spatial statistics is to predict a spatial quantile and its associated exceedance region. This has applications in environmental sciences, natural resources, and agriculture, since unusual events tend to have a strong impact on the environment. In this dissertation, we first review loss-function approaches to quantify exceedances. We then develop a method for the prediction of the spatial exceedance region involving a class of loss functions based on image metrics. We give special attention to Baddeley's loss function, for which we calibrate the choice of a tuning parameter. We then propose a joint-loss approach for the prediction of both a spatial quantile and its associated exceedance region. The optimal predictor is obtained by minimizing the posterior expected loss, given the spatial-trend, noise, and spatial-covariance parameters. In practice, the parameters are estimated and the minimization involves simulated annealing. We compare various predictors' performances through a simulation and apply our methodology to a spatial dataset of decadal temperature change over the Americas.