The Chiral Perturbation Theory (ChPT) has been very successful in describing low-energy hadronic properties in the non-perturbative regime of Quantum Chromodynamics. The results of ChPT, many of which are currently under active experimental investigation, provide stringent pre- dictions of many fundamental properties of hadrons, including quantities such as electromagnetic polarizabilities. The paper outlines our semi-automated calculations in ChPT, the corresponding results for the electric and magnetic polarizabilities of the proton and our predictions for Compton differential cross sections.