The spectrum of charmonium states -- particles composed of a bound charm and anti-charm quark -- has long served as a fundamental tool for studies of quarks and the strong force. The discovery of charmonium in the mid-1970's heralded the widespread acceptance of the reality of quarks. And contemporary advances in the precision of both experimental measurements and theoretical predictions have now allowed for meaningful quantitative inquiries into the workings of the strong force. But there are still a number of unresolved questions. Most strikingly, there are a number of new charmonium states, the "XYZ" states, that are yet to be fully interpreted. I will present a brief review of the importance of charmonium, what the new "XYZ" states could be telling us, and how the BESIII Experiment in Beijing, China is working to answer outstanding questions.