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According to QCD the quark structure of the nucleon spin within the \textit{twist-2} approximation is parameterized by eight transverse-momentum-dependent (TMD) parton distribution functions (PDFs). The PDFs describe the distributions of longitudinal and transverse momenta of partons and their correlations with nucleon and quark polarizations and can be accessed through measurement of spin (in)dependent azimuthal asymmetries in semi-inclusive DIS (SIDIS) and Drell-Yan processes. The COMPASS experiment at CERN, as part of its programme, addresses the exploration of the spin structure of the nucleon by measuring spin (in)dependent azimuthal asymmetries in semi-inclusive DIS and, recently, also in Drell-Yan processes. Between 2002 and 2011 COMPASS performed a series of SIDIS measurements, using a longitudinally polarized muon beam impinging on longitudinally and transversely polarized $^6LiD$ or $NH_3$ targets. Drell-Yan measurements with a $\pi^-$ beam interacting with a transversely polarized $NH_3$ target started with the 2015 run and will be continued in 2018. The measurement of the Sivers and other azimuthal asymmetries at practically the same hard scale in polarized SIDIS and Drell-Yan provides a unique possibility to test predicted in QCD (pseudo-)universal features of transverse-momentum-dependent parton distribution functions.  The main focus of this review is set on the first ever polarized Drell-Yan measurements performed by COMPASS and on the recent results obtained for target longitudinal and transverse spin dependent SIDIS asymmetries.

Measurement of target-polarization dependent azimuthal asymmetries in SIDIS and Drell-Yan processes at COMPASS experiment