Although we have a pretty good idea of what things are inside the center of our Milky Way within, say, 300 parsecs, we do not really understand how the various elements have evolved to get the way they are today. Why is there a vast rotating disk of molecular hydrogen spinning about the center? Why was there a violent episode of star forming activity there some 10 billion years ago? Why are stars continuing to form in such a hostile environment? How did the central black hole form? How is it that mass continues to flow into this region from the rest of the galaxy? What is the source of the energetic cosmic ray particles and 'synchrotron radiation' found there? Where did the vast magnetic field come from, and what accounts for its phenomenally well-organized shape despite the fact that the gas is sheared by the differential rotation of the Galactic center?
These are just a few of the questions that come to mind. There are many others which are related to the above big issues.