Abstract Up to now the COMPASS experiment of Abbon et al. (2007) [8] contributed with the muon beam to precise measurements of the nucleon longitudinal momentum structure. A more complete nucleon description beyond collinear approximation includes the quark intrinsic momentum distributions which are described by the Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs) and by Generalised Parton Distributions (GPDs). The next phase COMPASS Coll., (2010) [6] approved in December 2010 focuses on GPDs measurements through Deep Virtual Compton Scattering (DVCS) and Deep Virtual Meson Production (DVMP), in TMDs with Drell–Yan process and on Primakoff measurements. The latter shed light on the hadron structure through the hadron deformation in an external electromagnetic field described by the polarisabilities.