Recent data from the Tevatron collider have revealed that the producti
on rate of prompt charmonium at large transverse momentum is orders of
magnitude larger than the best theories of a few years ago had predic
ted. These surprising results can be understood by taking into account
two recent developments that have dramatically revised the theoretica
l description of heavy-quarkonium production. The first is the realiza
tion that fragmentation must dominate at large transverse momentum, wh
ich implies that most charmonium in this kinematic region is produced
by the hadronization of individual high-pr partons. The second is the
development of a factorization formalism for quarkonium production bas
ed on nonrelativistic QCD that allows the formation of charmonium from
color-octet c (c) over bar pairs to be treated systematically. This r
eview summarizes these theoretical developments and their implications
for quarkonium production in high-energy colliders.