The Status of Glueballs

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.