The high energy polarised muon beam available at CERN, with positive or negative charge, makes COMPASS a unique place for studies of General Parton Distributions (GPDs). The first GPD related COMPASS results were obtained for exclusive vector meson production on transversely polarised protons and deuterons. The data were taken in 2003-2010 with solid-state polarised targets, although without recoil detector. Results on various transverse target spin dependent azimuthal asymmetries are presented

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... and their relation to GPDs is discussed. The dedicated COMPASS GPD program started in 2012 with commissioning of a new long liquid hydrogen target and new detectors, such as the large recoil proton detector CAMERA and the large-angle electromagnetic calorimeter. It was followed by a short pilot 'DVCS run'. The performance of the setup and first results on DVCS channel are presented.