How do we present the concept of energy in physics?

Scientific and pedagogical comments about the fundamental physical concept of energy are made. In particular, we argue for an historical presentation of this concept because its essential justification is the research, conscious or not, of a characteristic quantity of a system whose fundamental property is to be conservative. Some delicate issues are clarified: the interest of potential energy associated with an external force, like the centrifugal one, and the meaning of internal energy are addressed. In this context, several examples in mechanics and thermodynamics are given: mechanical bifurcation, gas battery, radiation transfer, open systems and mass-energy in nuclear fusion