The latest measurements of the proton longitudinal spin structure function, g1p, in the deep inelastic (DIS) regime are presented. They improve the statistical accuracy of the existing data and extend the kinematic domain to a lower value of x and higher values of Q². A global NLO QCD fit of all g1 world data on the proton, deuteron and neutron has been achieved. The results give a quantification of the quark spin contribution to the nucleon spin, 0.26 < ΔΣ < 0.34 at 3 (GeV/c)² in MS scheme. The errors are dominated by the uncertainty on the shape of the functional forms assumed in the fit. A new verification of the fundamental Bjorken sum rule is obtained at a 9% level, using only COMPASS g1 proton and deuteron measurements. Preliminary results of a reevaluation of the gluon polarization Δg/g are presented. The analysis is based on double spin asymmetry of high-pT hadron production cross-sections in the DIS regime. A positive value of <Δg/g> = 0.113 ± 0.038 ± 0.035 is obtained at leading order at x ~ 0.1. In parallel, the double spin asymmetry in the photoproduction regime is also studied. Finally, preliminary results on quark fragmentation functions into pions extracted from a LO fit of pion multiplicities in semi-inclusive DIS are presented. [ABSTRACT FROM AUTHOR]