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 require 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 magnetohydrodynamic 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.