New results for the transverse target spin azimuthal asymmetry $A_{UT}^{\sin(\phi-\phi_S})$ for hard exclusive $\rho^0$-meson production on a transversely polarised NH$_3$ target will be presented. The measurement was performed in 2007 and 2010 with the COMPASS detector using the 160\,GeV/$c$ muon beam of the SPS at CERN. The asymmetry is sensitive to the nucleon helicity-flip generalised parton distributions $E^q$, which are related to the orbital angular momentum of quarks in the nucleon. The DVCS program of the future COMPASS-II experiment, dedicated to investigate the nucleon structure through Generalised Parton Distributions is presented as well. The high energy muon beam from CERN SPS allows to measure these processes in a wide and up to now uncovered range in Bjorken $x$ and $Q^2$. The availability of muon beams with opposite charges and polarisations provides unique possibilities to access the GPDs.