  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.
