The Galactic center GeV excess (GCE) detected by the Fermi Large Area Telescope is one of the most statistically significant and long-lasting anomalies in gamma rays. The origin of the excess is still in debate, and the leading interpretations include the self-annihilation of WIMP dark matter and prompt emission from a population of unresolved millisecond pulsars. In this talk, I will discuss some recent developments on constraining the origin of the excess. I will show that the inverse Compton emission caused by the relativistic e+/e- from millisecond pulsars provides a viable multi-wavelength handle for the origin of the GCE, and the Cherenkov Telescope Array could potentially detect such inverse Compton signal in the future.