Recent COMPASS results on Transverse Spin and Momentum dependent distributions and fragmentation functions

COMPASS is a fixed target experiment in operation at CERN since 2002 with a wide physics programme. By using either muon or hadron beams, both the study of the spin structure of the nucleon and hadron spectroscopy studies focusing on the search of exotic states are performed. An important part of this programme is the study of transverse spin and momentum dependent parton distribution and fragmentation functions (TMD PDFs and FFs). First measurements of HERMES and COMPASS showed sizeable Collins and Sivers asymmetries, allowing first extrac- tions of spin-dependent TMD PDFs and FFs. Now this field of research is entering the phase of precision measurements and is a central topic of many present and future experiments. Recent COMPASS results on Collins and Sivers asymmetries and on multidimensional analysis of SSA will be reviewed together with the perspective for future measurements