We show how the rotation emission from isolated interstellar Polycyclic Aromatic Hydrocarbons (PAHs) can explain the so-called anomalous microwave emission (AME). AME has been discovered in the last decade as microwave interstellar emission (10 to 70 GHz) that is in excess compared to the classical emission processes: thermal dust, free-free and synchrotron. The PAHs are the interstellar planar nano-carbons responsible for the near infrared emission bands in the 3 to 15 micron range. Theoretical studies show that under the physical conditions of the interstellar medium (radiation and density) the PAHs adopt supra-thermal rotation velocities, and consequently they are responsible for emission in the microwave range. The first results from the PLANCK mission unexpectedly showed that the AME is not only emitted by specific galactic interstellar clouds, but it is present throughout the galactic plane, and is particularly strong in the cold molecular gas. The comparison of theory and observations shows that the measured emission is fully consistent with rotation emission from interstellar PAHs. We draw the main lines of our PLANCK-AKARI collaborative program which intends to progress on this question by direct comparison of the near infrared (AKARI) and microwave (PLANCK) emissions of the galactic plane.