We describe the architecture and functionalities of a C++ software framework, coined PARTONS, dedicated to the phenomenology of Generalized Parton Distributions. These distributions describe the three-dimensional structure of hadrons in terms of quarks and gluons, and can be accessed in deeply exclusive lepto- or photo-production of mesons or photons. PARTONS provides a necessary bridge between models of Generalized Parton Distributions and experimental data collected in various exclusive production channels. We outline the specification of the PARTONS framework in terms of practical needs, physical content and numerical capacity. This framework will be useful for physicists – theorists or experimentalists – not only to develop new models, but also to interpret existing measurements and even design new experiments. The authors would like to thank P. Aguilera, S. Anvar, A. Besse, D. Chapon, R. Geraud, P. Guichon, K. Joo, A. Kielb, K. Kumericki, K. Passek-Kumericki and J.-Ph. Poli for many fruitful discussions and valuable inputs. This work was supported in part by the Commissariat a l'Energie Atomique et aux Energies Alternatives, by the French National Research Agency (ANR) grant ANR-12-MONU-0008-01, by the Grant No. 2017/26/M/ST2/01074 of the National Science Centre, Poland, and by the DOE grant DE-FG-04-ER41309.