Powerful winds driven by active galactic nuclei (AGN) are often invoked to play a fundamental role in the evolution of both supermassive black holes (SMBHs) and their host galaxies, quenching star formation and explaining the tight SMBH-galaxy relations. A strong support of this "quasar mode" feedback came from the recent X-ray observation of a mildly relativistic accretion disk wind in an ultraluminous infrared galaxy and its connection with a large-scale molecular outflow, providing a direct link between the SMBH and the gas out of which stars form. Spectroscopic observations, especially in the X-ray band, show that such accretion disk winds may be common in local AGN and quasars. However, their origin and characteristics are still not fully understood. Detailed theoretical models and simulations focused on radiation, magnetohydrodynamic (MHD) or a combination of these two processes to investigate the possible acceleration mechanisms and dynamics of these winds. Some of these models have been directly compared to X-ray spectra, providing important insights into the wind physics. Fundamental improvements on these studies will come from the unprecedented energy resolution and sensitivity of upcoming X-ray missions, such as Athena, and the synergy with future large facilities at other wavelengths, such as ALMA, E-ELT, SKA.