Are they real or are scientists still trying to determine for sure if they are there? I know it would make sense for them to be there for our current physics, but have they actually been measured and/or observed?

Evidence for gluons is good via colider experiments, but it is true that no free gluons have ever been observed. The earliest evidence is comes from 1979 and experiments at the electron-positron collider PETRA at DESY in Hamburg (see [1] for a recent review)

 

 

People are interested in a state of matter called quark-gluon plasma. As far as I know, there are some results to indicate that this state of matter has been achieved, but this is all rather tentative. I think the Brookhaven National Laboratory announced something not so long ago.

 

An even more direct observation would be to detect a glueball. As gluons are coloured it is possible that they can form bounded states without any quarks. Again here, any results are very tentative and glueballs, if they exist are very hard to detect.

 

 

References

 

[1] P. Söding, On the discovery of the gluon, The European Physical Journal H Volume 35, Number 1, 3-28