  The conventional color-singlet model was challenged by the recent data on
quarkonium production. Discrepancies in production rates were observed at the
Tevatron, at LEP, and in fixed-target experiments. The newly advocated
color-octet mechanism provides a plausible solution to the anomalous quarkonium
production observed at the Tevatron. The color-octet mechanism should also
affect other quarkonium production channels. In this paper we will summarize
the studies of quarkonium production in $Z^0$ and $\Upsilon$ decays.
