  We review different constrained versions of the NMSSM: the fully constrained
cNMSSM with universal boundary conditions for gauginos and all soft scalar
masses and trilinear couplings, and the NMSSM with soft terms from Gauge
Mediated Supersymmetry Breaking. Regarding the fully constrained cNMSSM, after
imposing LEP constraints and the correct dark matter relic density, one single
parameter is sufficient to describe the entire Higgs and sparticle spectrum of
the model, which then contains always a singlino LSP. The NMSSM with soft terms
from GMSB is phenomenologically viable if (and only if) the singlet is allowed
to couple directly to the messenger sector; then various ranges in parameter
space satisfy constraints from colliders and precision observables. Motivations
for and phenomenological features of extra U(1)' gauge symmetries are briefly
reviewed.
