Studying the AGN feedback effect on the cold molecular gas of their host galaxies is key to understanding its impact on the local star formation. I will present a study of the CO(2-1) emission line distribution and kinematics in a sample of four local Seyfert galaxies with luminosities L_AGN ~ 10^44 erg/s. They were observed with ALMA, using a spatial resolution of ~100 – 400 pc, and covering up to ~10 kpc radii. Comparing the CO(2-1) observations with imaging data of [O III]lambda5007 emission lines from HST, we find that the ionized gas is generally observed in regions deficient in molecular gas, which we interpret to be caused by the AGN radiation partially destroying it. Although the kinematics of the cold molecular gas is dominated by rotation, all Seyfert galaxies present regions with double peaks in CO(2-1), which trace clouds with more complex motions. In particular, for NGC 3281 and NGC 6860, the cold molecular gas outflows were detected at the edges of their bipolar [O III] emission, surrounding it. I will also discuss my ongoing project to analyze the complex kinematics of the ionized gas in high-redshift radio galaxies (z ~ 3) obtained with JWST.