  The quest for the elusive dark matter (DM) that permeates the Universe (and
in general the search for signatures of Physics beyond the Standard Model at
astronomical scales) provides a unique opportunity and a tough challenge to the
high-energy astrophysics community. In particular, the so-called DM indirect
searches - mostly focused on a class of theoretically well-motivated DM
candidates such as the weakly-interacting massive particles - are affected by a
complex astrophysical background of cosmic radiation. The understanding and
modeling of such background requires a deep comprehension of an intricate
classical plasma physics problem, i.e. the interaction between high-energy
charged particles, accelerated in peculiar astrophysical environments, and
magneto-hydrodynamic turbulence in the interstellar medium of our Galaxy. In
this review we highlight several aspects of this exciting interplay between the
most recent claims of DM annihilation/decay signatures from the sky and the
Galactic cosmic-ray research field. Our purpose is to further stimulate the
debate about viable astrophysical explanations, discussing possible directions
that would help breaking degeneracy patterns in the interpretation of current
data. We eventually aim to emphasize how a deep knowledge on the physics of CR
transport is therefore required to tackle the DM indirect search program at
present and in the forthcoming years.
