The electromagnetic properties of the nucleon arise from its composite nature. External electric and magnetic fields induce dipole moments described by the scalar polarizabilities ($\alpha_N$ and $\beta_N$), while the response of the nucleon spin is described by four spin polarizabilities. Consequently, studying these observables offers a window into the interaction among the constituent charges and currents in the nucleon, described theoretically by Quantum Chromodynamics (QCD). In particular, high-precision measurements of the scalar and spin polarizabilities provide a means for studying the low-energy, non-perturbative regime of QCD. Such measurements are needed to constrain emerging calculations from lattice QCD and Chiral Effective Field Theories and are critical inputs to descriptions of the proton-neutron mass difference. To this end, a program of Compton scattering experiments on light nuclei is underway at the High Intensity Gamma Source (HI$\gamma$S) at Duke University, with the aim of providing the world's most precise data to extract the polarizabilities.