  Calculations within QCD (lattice and sum rules) find the lightest glueball to
be a scalar and with mass in the range of about 1000-1700 MeV. Several
phenomenological investigations are discussed which aim at the identification
of the scalar meson nonets of lowest mass and the super-numerous states if any.
Results on the flavour structure of the light scalars f0(500), f0(980) and
f0(1500) are presented; the evidence for f0(1370) is scrutinized. A significant
surplus of leading clusters of neutral charge in gluon jets is found at LEP in
comparison with MCs, possibly a direct signal for glueball production; further
studies with more energetic jets at LHC are suggested. As a powerful tool in
the identification of the scalar nonets or other multiplets, along with signals
from glueballs we propose the exploration of symmetry relations for decay rates
of C=+1 heavy quark states like chi-c or chi-b. Results from chi-c decays are
discussed; they are not in support of a tetra-quark substructure of f0(980). A
minimal scenario for scalar quarkonium - glueball spectroscopy is presented.
