  We discuss the $U(1)_X$ extensions of the standard model with focus on the
Stueckelberg mechanism for mass growth for the extra $U(1)_X$ gauge boson. The
assumption of an axionic connector field which carries dual U(1) quantum
numbers, i.e., quantum numbers for the hypercharge $U(1)_Y$ and for the hidden
sector gauge group $U(1)_X$, allows a non-trivial mixing between the mass
growth for the neutral gauge vector bosons in the $SU(2)_L\times U(1)_Y$ sector
and the mass growth for the vector boson by the \st mechanism in the $U(1)_X$
sector. This results in an extra $Z'$ which can be very narrow, but still
detectable at the Large Hadron Collider (LHC). The $U(1)_X$ extension of the
minimal supersymmetric standard model is also considered and the role of the
Fayet-Illiopoulos term in such an extension discussed. The $U(1)_X$ extensions
of the SM and of the MSSM lead to new candidates for dark matter.
