Generalized continua represent a class of models whose potential applicability seems to have been underestimated. The mathematical structure of these models is discussed and the reasons why it has been underestimated are made clear. Their importance in the theory of metamaterials is highlighted and their potential impact on future technological applications is carefully argued. It is shown how the original ideas of Lagrange and Piola can be developed by using the modern tools of differential geometry, as formulated by Ricci and Levi-Civita. It has to be concluded that variational principles are the most powerful tool also in the mathematical modeling of metamaterials.