This talk presents research in spatial statistics and extreme value statistics and gives a brief introduction to both fields. Despite a great deal of literature in these two areas, research in their intersection has progressed at a slower pace and is particularly challenging, but spatial extremes is especially important in light of climate change. First, we discuss a scalable model for nonstationary multivariate Gaussian Processes which is applied to a large climate ensemble consisting of 40 variables. Second, we discuss a nonstationary model for univariate extremes which is applied to observational daily mean temperature data at seven different cities with distinct local climates. Unlike traditional extremes methodology, which considers only the upper tail of the distribution, this parametric model fits the entire distribution. Finally, we discuss a bivariate spatial extremes model which focuses on negatively-dependent teleconnections where Alaska is very warm while the midlatitudes of North America are very cold.