  We discuss the theoretical expectations and phenomenological evidence for the
lightest glueballs and the members of the meson nonet with quantum numbers
J^PC=0^{++}. We reconsider the recent evidence for candidate states with masses
below ~1700 MeV, but include also the results from earlier 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^{++} glueball. This state together with
eta(1440) and f_J(1710) with spin J=2 form the basic triplet of binary gluonic
bound states. We argue that these hypotheses are consistent with what can be
expected theoretically.
