Understanding the formation of (exo)-planetary systems requires the combined effort of advanced computational models and high-resolution multi-wavelength observations. In my talk, I will review our current understanding of the dynamic evolution of protoplanetary disks. 3D multi-physics simulations and high-performance computing allow us to study the thermal and kinematical evolution of young circumstellar disks and planets' birthplaces in detail. I will also highlight why the inner disk regions, especially those close to the silicate sublimation, are crucial for forming terrestrial planets. Those unable to attend the colloquium in person are invited to participate online through Zoom (Meeting ID: 942 0262 2849, passcode 792771) using the link: https://eu02web.zoom-x.de/j/94202622849?pwd=dGlPQXBiUytzY1M2UE5oUDRhbzNOZz09