The three-dimensional quark and gluon structure of hadrons is a driving motivation for experimental programs currently run at Jefferson Laboratory and at CERN. The con- cept of Generalized Parton Distributions promises an understanding of the generation of the charge, spin, and energy-momentum structure of hadrons by their fundamental constituents. Forthcoming measurements with unprecedented accuracy will challenge our quantitative understanding of the large-distance regime of QCD. To fully exploit these fu- ture experimental data, and actually learn about QCD, new tools and models are currently being developed.
After a brief reminder of what make Generalized Parton Distributions a unique tool to probe the structure of hadrons, we will explain why it is so hard to model them, and sketch some recent progresses. In particular we will discuss various equivalent parameterizations and give a status of the Dyson-Schwinger approach. We will also review the constraints provided by existing measurements, and describe the tools required to deal with the future high precision data expected in the valence region from Jefferson Laboratory.