The status of glueballs

Calculations within QCD (lattice and sum rules) find the lightest glueball to be a scalar 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 f(0)(500), f(0)(980) and f(0)(1500) are presented; the evidence for f(0)(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 f(0)(980). A minimal scenario for scalar quarkonium-glueball spectroscopy is presented.