2016 by Taylor & Francis Group, LLC. Many problems involve dependent extremes, such as extreme precipitation, heavy snow, financial and insurance risk, to name a few. These problems motivate the need for the development of statistical modeling and inference tools for multivariate ex treme values. Copula models and max-stable process models have become two pop ular modeling choices to characterize the dependence among multivariate extremes, especially for high-dimensional cases. Despite the sound mathematical properties of these models in terms of modeling tail dependence among multivariate extreme val ues, likelihood inference is challenging for such models because their correspond ing joint likelihood functions are unavailable. Taking advantage of the availability of the low-dimensional marginal likelihoods, the composite likelihood approach has become a major inference tool for max-stable process models. In this chapter, we review the concepts of composite likelihoods and present some recent developments of composite likelihood approaches for the inference of max-stable process models with illustrative examples. We also discuss the use of composite likelihood for the inference of copulas for modeling multivariate extreme values.