Recent molecular line observations with ALMA and NOEMA in several Brightest Cluster Galaxies (BCG) have revealed the large-scale filamentary structure at the center of cool core clusters. These filaments extend over 20-100kpc, they are tightly correlated with ionized gas (Hα, [NII]) emission, and have characteristic shapes: either radial and straight, or also showing a U-turn, like a horse-shoe structure. The kinematics is quite regular and laminar, and the derived infall time is much longer than the free-fall time. The filaments extend up to the radius where the cooling time becomes larger than the infall time. Filaments can be perturbed by the sloshing of the BCG in its cluster, and spectacular cooling wakes have been observed. Filaments tend to occur at the border of cavities driven in the X-ray gas by the AGN radio jets. Observations of cool core clusters support the thermal instability scenario, which accounts for the multiphase medium in the upper atmospheres of BCG, where the right balance between heating and cooling is reached, and a chaotic cold gas accretion occurs. Molecular filaments are also seen associated to ram-pressure stripped spiral galaxies in rich galaxy clusters, and in jet-induced star formation, suggesting a very efficient molecular cloud formation even in hostile cluster environments.