Nuclear Star Clusters (NSCs) are prevalent in nearby galaxies of any morphological type. The origin of NCSs remains an open question, but it is generally thought that their formation and evolution are closely related to the seeding and growth of a central (super-)massive black hole (SMBH). The nearest example of a NSC is found in the center of our own Galaxy, which offers the best opportunity to study a wide range of physical processes and intriguing phenomena unique to the immediate vicinity of a SMBH. In this talk, I will introduce our recent effort, based primarily on Chandra X-ray observations and hydrodynamic simulations, in understanding the origin of specific stellar populations (Wolf-Rayet stars, XRBs and supernova remnants) in the Milky Way NSC and their potential impact on the Galactic Center environment. When time permits, I will also touch on related topics in the scope of globular clusters and extragalactic NSCs.