Quarkonium production via fragmentation: A review

We review the physics of quarkonium production at high energy colliders, with a specific emphasis on production $via$ fragmentation. We discuss the fragmentation picture for the production of quarkonia at large-$p_T$ at the Tevatron and emphasise the importance of the colour-octet components of the quarkonium wave function which are included in the fragmentation functions. Applications of these theoretical ideas to other processes, both at the Tevatron and at other experiments like LEP, HERA and the LHC are important as they will provide stringent tests of these ideas.