Our knowledge of the nucleon spin structure has greatly improved over the last twenty years or so, but still many fundamental questions remain unsolved. This means that one has to fully understand it, in terms of the basic partonic constituents of the nucleon, considering the spin as a fundamental quantum number. Simultaneously, the spin sector of the underlying dynamical theory, i .e. perturbative QCD, must be tested at the highest possible precision level. Our current activities in QCD spin physics involve, in particular, the phenomenological description of polarized parton distributions in the framework of a statistical approach, which was first proposed in 2002. It can be applied equally well to unpolarized and polarized data, a rather unique situation, and it is valid in a wide kinematical range in x and Q2. It has, so far, a very good predictive power, for both Deep Inelastic Scattering and hadronic collisions recent results. We are also closely associated to the physics programme of the polarized pp collider at RHIC − BNL, operating since 2001, for the measurement of double helicity and single transverse spin asymmetries. It has reached the energy of √8=500GeV, allowing the gauge bosons W± and Z production and the measurement of the parity-violating asymmetries. We have also a strong interest in the experimental physics programmes of COMPASS (CERN) and JLab upgrade. which will investigate the poorly known high-x region. Finally, let us mention a related topic, namely the systematic study of positivity conditions for spin observables (see Physics Reports 470,1-92 (2009)), which reduces the allowed domain of values, as first observed in 1995 for the case of the quark transversity distributions (Physical Review Letters 74,1292-1294 (1995).