Active galactic nuclei are the most numerous sources of the extragalactic gamma-ray sky. They are also in the spotlight of the multi-messenger astronomy as they are candidate sources to emit high-energy astrophysical neutrinos and ultra-high-energy gamma-rays. The observed variability from radio to VHE gamma-rays can be used to constrain the particle acceleration and emission mechanisms, but this requires extensive multiwavelength observations of a large sample of sources. In this talk, I will present our recent study on the connection between radio flares from blazars and astrophysical neutrinos.  I will also present the the methodology that allows us to systematically compare particle acceleration simulations with state of art observations. Finally, I will highlight the major leap forward that the Cherenkov Telescope Array very high-energy gamma-ray observations of AGN will bring us.