We compute the masses and decay widths of the gluonia using QCD spectral sum rules and low-energy theorems. In the scalar sector, one finds a gluonium having a mass MG = (1.5 ± 0.2) GeV, which decays mainly into the U(1)A channels ηη′ and 4π0. However, for a consistency of the whole approach, one needs broad low-mass gluonia (the σB and its radial excitation), which couple strongly to the quark degrees of freedom similarly to the η′ of the U(1)A sector. Combining these results with the ones for the q¯q quarkonia, we present maximal gluonium-quarkonium mixing schemes, which can provide quite a good description of the complex spectra and various decay widths of the observed scalar mesons σ(1.), f0(0.98), f0(1.37), f0(1.5) and fJ(1.71). In the tensor sector, the gluonium mass is found to be MT ⋍ (2.0±0.1) GeV, which makes the ζ(2.2) a good 2++ gluonium candidate, even though we expect a rich population of 2++ gluonia in this region. In the pseudoscalar channel, the gluonium mass is found to be Mp ⋍ (2.05 ± 0.19) GeV, while we also show that the E/ι(1.44) couples more weakly to the gluonic current than the η′(0.96), which can favour its interpretation as the first radial excitation of the η′(0.96).