  In this paper we discuss the evolution of breakup models from fully quantum
mechanical, such as the Ichimura-Austern-Vincent model to semiclassical, to
eikonal approximations following the insight on the mechanism first proposed by
Hussein and McVoy (HM) for the presently called stripping term. In particular
we concentrate on, and stress that, the correct implementation of a quantum
mechanical model of breakup requires the use of energy dependent interactions
and the energy averaging procedure is a key point to understand the difference
among models. On the other hand using fixed energy potentials is one of the
steps towards the high energy eikonal limit first proposed by HM. However the
intermediate semiclassical transfer to the continuum model (STC) of Bonaccorso
and Brink does use an energy dependent nucleon-target optical potential, while
fixing the core-target interaction at the incident energy. The relationship
between these methods is clarified.
