Exotic mesons are mesons that have quantum numbers not possible in the quark model; some proposals for non-standard quark model mesons could be: glueballs or gluonium Glueballs have no valence quarks at all. tetraquarks Tetraquarks have two valence quark–antiquark pairs. hybrid mesons Hybrid mesons contain a valence quark–antiquark pair and one or more gluons. All exotic mesons are classed as mesons because they are hadrons and carry zero baryon number. Of these, glueballs must be flavor singlets – that is, must have zero isospin, strangeness, charm, bottomness, and topness. Like all particle states, exotic mesons are specified by the quantum numbers which label representations of the Poincaré symmetry, q.e., by the mass (enclosed in parentheses), and by , where is the angular momentum, is the intrinsic parity, and is the charge conjugation parity; One also often specifies the isospin of the meson. Typically, every quark model meson comes in SU(3) flavor nonet: an octet and an associated flavor singlet. A glueball shows up as an extra (supernumerary) particle outside the nonet. In spite of such seemingly simple counting, the assignment of any given state as a glueball, tetraquark, or hybrid remains tentative even today, hence the preference for the more generic term exotic meson. Even when there is agreement that one of several states is one of these non-quark model mesons, the degree of mixing, and the precise assignment is fraught with uncertainties. There is also the considerable experimental labor of assigning quantum numbers to each state and crosschecking them in other experiments. As a result, all assignments outside the quark model are tentative. The remainder of this article outlines the situation as it stood at the end of 2004. Lattice predictions Lattice QCD predictions for glueballs are now fairly settled, at least when virtual quarks are neglected. The two lowest states are 0++ with mass of and 2++ with mass of The 0−+ and exotic glueballs such as 0−− are all expected to lie above . Glueballs are necessarily isoscalar, with isospin = 0. The ground state hybrid mesons 0−+, 1−+, 1−−, and 2−+ all lie a little below . The hybrid with exotic quantum numbers 1−+ is at . The best lattice computations to date are made in the quenched approximation, which neglects virtual quarks loops. As a result, these computations miss mixing with meson states. 0++ states The data show five isoscalar resonances: (500), (980), (1370), (1500),