  Production cross sections of heavy quarkonia are considered as useful tools
to study various aspects of QCD. We have entered a new era of quarkonium
production phenomenology, with the help of new measurements from the LHC giving
access to more varieties of observables, and recent theoretical developments
that provided us a better understanding of the short-distance process in which
quarkonia are produced. With a more concrete understanding of perturbative
corrections and a prolific collection of data, a satisfactory description of
the quarkonium production mechanism might now be within reach. Unfortunately,
the exact mechanism of quarkonium production still remains elusive. Even
analyses based on the same formalism can lead to different descriptions of the
production process and give contradicting predictions of processes involving
heavy quarkonia. This implies that there are much more physics yet to be
understood and much work yet to be done in quarkonium production phenomenology.
In this paper, we review the current status of theoretical approaches and
discuss possible strategies that may improve our understanding of heavy
quarkonium production.
