In this talk I will review the most relevant results obtained in arXiv:1411.7623 and arXiv:1504.00227.

In particular, I will focus on the possibility to use the gamma-ray data collected by the Fermi Large Area Telescope as a probe to investigate non-standard properties of cosmic-ray diffusion in the Milky Way galaxy. Furthermore, I will discuss important implication related to the ultra-high energy neutrino events detected by the IceCube experiment.

The seminar, although technical in various aspects, is addressed to a broad audience.