Introduced in the 1990s, Generalised Parton Distributions (GPDs) have been deeply studied both theoretically and experimentally since then. Several phenomenological models have emerged, among them those based on the so-called Double Distributions (DDs), which have the advantage to easily fulfil some of the GPDs theoretical constraints.
In this work, the ambiguity in the definition of the Double Distribution is highlighted and then used as an additional degree of freedom for modeling GPDs. The resulting models allow one to better describe some of the available experimental data coming from JLab Hall A DVCS collaboration than the previous DDs-based models. However, additional experimental data are required to exploit the entire potential of these new parameterisations. A first step has also been done toward a dynamical description of the structure of hadrons. Using the Dyson-Schwinger equations, it has been possible to compute analytically the pion GPD within the triangle diagram approximation. The comparison with available data (Form factor and PDF) appears to be very good. Still, the algebraic starting point contains weaknesses which have been identified and are under controlled. It has been thus possible to compute the probability density to find a quark at a given position in the transverse plan carrying a given momentum fraction. Finally, perspectives on lightcone computations are given at the end of this work.