  In this note we summarize some of the quantum properties found since the
early 80's until nowdays that characterize at quantum level the spectrum of the
supermembrane. In particular we will focus on a topological sector of the 11D
supermembrane that, contrary to the general case, has a purely discrete
spectrum at supersymmetric level. This construction has been consistently
implemented in different types of backgrounds: toroidal and orbifold-type with
G2 structure able to lead to a true G2 compactification manifold. This theory
has N=1 supersymmetries in 4D. comment on the relevant points of this
construction as well as on its spectral characteristics. We will also make some
comments on the quantum properties of some effective formulation of multiple
M2's theories recently found.
