This article presents the review of the current understanding on the
pion-nucleon Drell-Yan process from the point of view of the TMD factorization.
Using the evolution formalism for the unpolarized and polarized TMD
distributions developed recently, we provide the theoretical expression of the
relevant physical observables, namely, the unpolarized cross section, the
Sivers asymmetry, and the cos2ϕ asymmetry contributed by the double
Boer-Mulders effects. The corresponding phenomenology, particularly at the
kinematical configuration of the COMPASS πN Drell-Yan facility, is
displayed numerically.Comment: Version published in Advances in High Energy Physic