  The quasiconformal method provides us with a unified approach to the
construction of minimal unitary representations (minrep) of noncompact groups,
their deformations as well as their supersymmetric extensions. We review the
quasiconformal construction of the minrep of SO(d,2), its deformations and
their applications to unitary realizations of AdS_{(d+1)}/CFT_d higher spin
algebras and their deformations for arbitrary d and supersymmetric extensions
for dimensions d less than seven. AdS_{(d+1)}/CFT_d higher spin algebras, their
deformations and supersymmetric extensions are given by the enveloping algebras
of the quasiconformal realizations of the minrep, its deformations and
supersymmetric extensions, respectively, and are in one-to-one correspondence
with massless conformal fields for arbitrary d and massless conformal
supermultiplets for dimensions d less than seven.
