In recent years, copula models are being used in all areas of human endeavors including energy, environment, social, natural and physical sciences. Copulas are the most powerful tools that can model dependent structures between various complex correlated variables. In this paper, we specifically examine the development of copula models and their applications in the areas of energy, fuel cells, forestry and environmental sciences. It reviews the latest literature on the types of copula models, including Gumbel, Clayton, Frank, Gaussian, vine, and the theoretical development of a mixture of bivariate and multivariate copula distributions, in terms of both static and dynamic applications. A comparative review of literature is done using ARMA, DCC, and GARCH models relative to copulas. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.