Llanes Estrada, Felipe José2023-06-172023-06-172021-06-011951-635510.1140/epjs/s11734-021-00143-8https://hdl.handle.net/20.500.14352/8273© 2021 Springer Heidelberg This publication is supported by EU Horizon 2020 research and innovation programme, STRONG-2020 project, under grant agreement No 824093; grants MINECO:FPA2016-75654-C2-1-P, MICINN: PID2019-108655GB-I00, PID2019-106080GB-C21 (Spain); Universidad Complutense de Madrid under research group 910309 and the IPARCOS institute.This compact review about gluonium focuses on a slate of theoretical efforts; among the many standing works, I have selected several that are meant to assist in the identification, among ordinary mesons, of the few Yang-Mills glueball configurations that populate the energy region below 3 GeV. This includes J/psi radiative and vector-meson decays, studies of scalar meson mixing, of high-energy cross-sections via the Pomeron and the odderon, glueball decays, etc. The weight of accumulated evidence seems to support the f(0)(1710) as having a large (and the largest) glueball component among the scalars, although no single observable by itself is conclusive. Further tests would be welcome, such as exclusive f(J) production at asymptotically high s and t. No clear experimental candidates for the pseudoscalar or tensor glueball stand out yet, and continuing investigations trying to sort them out will certainly teach us much more about mesons.engjournal articlehttp://dx.doi.org/10.1140/epjs/s11734-021-00143-8https://link.springer.com/open access53Scattering cross-sectionPseudoscalar glueballScaling lawsForm-factorsScalarQcdMassesSpectrumOdderonPomeron.Física (Física)22 Física