The COMPASS experiment at CERN is studying since 2002 the spin structure of the nucleon, both for longitudinal and transverse nucleon spin. In the first case, the measurements of DIS and SIDIS asymmetries, including also high-pT hadron production and D0 mesons, allow to access the nucleon longitudinal PDFs, their first moments and the gluon polarization. The LO analysis, performed by COMPASS have shown that ?g/g is small around xg ? 0.1, and its first moment should not be larger than 0.2 ? 0.3 in absolute value. Transverse spin effects have rised large interest in the last 10 years and the measurements performed have shown evidence for new phenomena, associated with transverse momentum dependent distribution and fragmentation functions. Col...