The aim of the present paper is to illustrate the modern state of variational calculus in large with several physical and geometrical examples. In spite of the great progress in variational calculus during the last century, some classical variational problems are still far from its final solution. But, as it often happens in Science, the attempts to solve classical problems give rise to beautiful theories that give us an understanding of the problems and, sometimes, lead to unexpected discoveries. As typical examples we have chosen Minimal Surfaces Theory and Extreme Networks Theory that attract the attention of many scientists during several ages.