I am interested in modeling the dynamics of massive black hole binaries (MBHs) that originate from galaxy mergers. To address this problem, I will combine high-resolution numerical simulations with semi-analytical modeling. On the numerical side, I will use codes such as KETJU to capture the complex interplay between galaxy formation and black hole evolution. In parallel, I will develop semi-analytical models to describe the inspiral of MBH binaries under the emission of gravitational waves, explicitly incorporating perturbative environmental effects from the surrounding medium. By combining these complementary approaches, my work aims to connect the astrophysical evolution of MBHs to their relativistic dynamics, ultimately providing robust predictions for gravitational-wave signals detectable by the upcoming LISA mission.