  In the past fifteen years, the way to study TeV gamma-ray emitters changed
drastically. The detection-based approach aimed at populating the TeV gamma-ray
sky evolved into a physics-driven one, with the ambitious objective of
understanding the mechanisms responsible for the emission and their
environments. The synergic collaboration between instruments operating in
different electromagnetic bands and with different messengers is therefore
crucial. In this talk, I will report highlights on extragalactic physics
studies achieved with the MAGIC telescopes, with special emphasis on the
MeV-TeV connection.
