We discuss the theoretical expectations and phenomenological evidence for t
he lightest glueballs and the members of the meson nonet with quantum numbe
rs J(PC) = O++ . We reconsider the recent evidence for candidate states wit
h masses below similar to 1700 MeV, but include also the results from earli
er phase-shift analyses. Arguments are presented to classify the scalars f(
0)(980) and f(0)(1500) as members of the 0(++) nonet, with a mixing rather
similar to that of the pseudoscalars eta' and eta. The S-wave states called
f(0)(400 - 1200) and f(0)(1370) are considered as different signals from a
single broad resonance, which we take to be the lowest-lying 0(++) gluebal
l. This state together with eta(1440) and f(J)(1710) with spin J = 2 form t
he basic triplet of binary gluonic bound states. We argue that these hypoth
eses are consistent with what can be expected theoretically.