COMPASS is a fixed target experiment at CERN dedicated to studies of the spin structure of the nucleon and of the spectroscopy of hadrons. High energy polarized muon beams available at CERN and the option of using either positive or negative ones, give an excellent opportunity for studying GPD, through the DVCS process and the HEMP reaction. The first result of COMPASS GPD programme came from transverse target-spin asymmetries measured in hard exclusive ρ0 production using a transversely polarized proton target. Recent results on transverse target-spin asymmetries for the exclusive ω production are presented as well. Projections of the achievable accuracies and preliminary results of 2012 DVCS pilot run measurements are discussed. Beginning of that run was devoted to commissioning of the long (2.5 m) liquid hydrogen target and new detectors, the large recoil proton detector and large angle electromagnetic calorimeter. These detectors will be a backbone for the future measurements of exclusive processes during the dedicated data taking in 2016–2017.