The standard theory of colour forces (QCD) suggests that in addition to the familiar hadrons made of quarks, there should exist new states where coloured gluons play an essential dynamical role. I review the theoretical predictions for the properties of these 'glueballs' and of states containing resonating quarks and gluons (variously called 'hybrids', 'hermaphrodites' or 'meiktons'). I attempt to highlight those features which are common to several models in the literature. Experimental candidates are confronted with the models. No clearcut signal for a gluonic hadron yet exists; consequently I consider what future data are required to determine the constituency of some popular candidates.

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