A fundamental property of the proton involves the system's response to an external electromagnetic (EM) field. It is characterized by the EM polarizabilities
that describe how easily the charge and magnetization distributions inside the system are distorted by the EM field, such as during the Compton scattering with a real photon. When the polarizabilities are generalized to finite momentum transfer by replacing the incoming real photon of the Compton scattering process with a space-like virtual photon, they map out the deformation of the quark densities in a proton subject to an EM field. They shed light to the underlying system dynamics and provide a key for decoding the proton structure in terms of the theory of the strong interaction that binds quarks and gluons together. Recent experimental measurements at Jefferson Lab have provided high precision data, that offer guidance and present significant challenges to nuclear theory. Future experiments aim to improve further the study of the generalized polarizabilities, both in terms of the kinematic range as well as on the level of the experimental precision.