It has been argued in the Introduction that a good starting point to develop a practically meaningful nonlinear control theory is to specialize the class of systems under consideration. The main reason being, of course, that the vast array of nonlinear systems renders futile the quest of a monolithic theory applicable for all systems. In particular, it defies the approach of mimicking the, by now fairly complete, linear theory. Specializing the systems, on the other hand, introduces additional constraints and structure, which may enable otherwise intractable problems to be answered. In this chapter we describe the class of systems that we will consider throughout the book and which we call Euler-Lagrange (EL) systems. The most important reason for singling out the study of EL systems is that they capture a large class of contemporary engineering problems, specially some which are intractable with linear control tools. Finally, by restricting ourselves to systems with physical constraints we believe we can contribute to reverse the tide of "find a plant for my controller" which still permeates most of the research on control of general nonlinear systems.