  We review recent progress on the study of quarkonium production with the STAR
detector. We discuss the results of a J/psi -> e+e- test trigger for p+p
collisions during Run V at RHIC. For the Au+Au data from Run IV, we discuss the
implementation of a test trigger for Upsilon -> e+e-. We obtain an upper limit
on Upsilon production from the test trigger data. The prospects for future runs
with upgraded detectors are outlined.
