Transversity and Lambda polarization

Two related issues are discussed, which might be easily explored by present and future COMPASS experiments. The first one deals with the new world of transversity, the fundamental polarized parton distribution so far totally unknown. The second issue concerns Lambda production in polarized semi-inclusive processes, with a measurement of the Lambda polarization, which might give novel information on distribution and fragmentation properties of polarized partons. In case of transverse polarization the detection of Lambda's gives access to a new way of measuring transversities. Also the interesting case of Lambda polarization in unpolarized processes is discussed.