Double quantum wells are among the simplest semiconductor heterostruct
ures exhibiting tunnel coupling. The existence of a quantum confinemen
t effect for the energy levels of a narrow single quantum well has bee
n largely studied. In double quantum wells, in addition to these confi
nement effects which characterize the levels of the isolated wells, on
e faces the problem of describing the eigenstates of systems interacti
ng weakly through a potential barrier. In addition, the actual structu
res differ from the ideal systems studied in the quantum mechanics tex
tbooks in many aspects. The presence of defects leads, for instance, t
o an irreversible time evolution for a population of photocreated carr
iers, This irreversible transfer is now clearly established experiment
ally. The resonant behaviour of the transfer has also been evidenced,
from the study of biased structures. If the existence of an interwell
transfer is now clearly established from the experimental point of vie
w, its theoretical description, however, is not fully satisfactory. Th
is review focuses on the theoretical description of the energy levels
and of the interwell assisted transfer in double quantum wells. We sha
ll firstly outline the problem of tunnel coupling in semiconductor het
erostructures and then discuss the single particle and exciton eigenst
ates in double quantum wells. In the remaining part of the review we s
hall present and critically review a few theoretical models used to de
scribe the assisted interwell transfer in these structures.