We study the dynamics in the dense nuclear star cluster that surrounds SuperMassive Black Holes (SMBH) in the center of galaxies. We focus on the interplay between two-body scatterings and Gravitational Waves (GWs) emission and its implications on the abundance of EMRIs and their characteristics, such as the strain, the eccentricity distribution, and so on. Finally, we focus on the immediate surrounding of the SMBH to study the final stages of extreme mass-raio binary maergers. Using the fact that toward the merger small mass-ratio binary systems tend to a geodesic universal infall (GUI) trajectory, we perform our analysis directly in the test-particle limit. Thus, we calaulate the GW waveform and determine the post-merger mass, spin and linear momentum of the remnant black hole.