In this chapter, the authors present two local-diagnostics techniques. The first one are local-fidelity plots that evaluate the local predictive performance of the model around the observation of interest. The second one are local-stability plots that assess the stability of predictions around the observation of interest. The idea behind local-stability plots is to check whether small changes in the explanatory variables, as represented by the changes within the set of neighbors, have got much influence on the predictions. For a high-dimensional setting, an interesting alternative is the proximity measure used in random forests, as it takes into account variable importance; however, it requires a fitted random forest model. Local-stability plots may be very helpful to check if the model is locally additive, as for such models the CP profiles should be parallel. The disadvantage of both types of plots is that they are quite complex and lack objective measures of the quality of the model-fit.