Glueballs are the most obvious, but this far not fully tested prediction of Quantum Chromodynam-
ics. The lowest expected glueball states, in particular 0++ states are difficult to characterize, since they share the quantum numbers of the "vacuum" and of a number of possible quark-antiquark states. In this paper, we argue that the more easily identifiable exotics provide us with strong hints on the way to pursue the chase, and in particular the relation with quantum anomalies and the 𝜂 and 𝜂′ states.