In this joint experimental and ab initio study, we investigated the influence of chemical composition and martensitic phase transition on the electronic, magnetic, optical and magneto-optical properties of ferromagnetic shape-memory Ni-Mn-Sn alloys. Optical properties and polar magneto-optical Kerr effect (MOKE) spectra for Ni-Mn-Sn alloy film of composition NiMnSn deposited epitaxially on MgO(0 0 1) substrate were measured over the photon energy range [Formula: see text] eV, and the complete set of optical conductivity tensor elements were determined. To explain the microscopic origin of the optical and magneto-optical spectra, extensive first-principles calculations were made, using the spin-polarized fully relativistic linear-muffin-tin-orbital method. The electronic, magnetic and magneto-optical properties of Ni-Mn-Sn Heusler alloys were investigated for the cubic austenitic and 4O orthorhombic martensitic phases, in stoichiometric and off-stoichiometric compositions. The MOKE properties of Ni-Mn-Sn systems are very sensitive to deviation from stoichiometry. It was shown that the ab initio calculations reproduce experimental spectra well, and help to explain the microscopic origin of Ni-Mn-Sn optical and magneto-optical responses. The interband transitions responsible for the prominent structures in the Ni-Mn-Sn MOKE spectra have been identified-they come from relatively narrow energy intervals at several well-defined vicinities of high-symmetry directions of the Brillouin zone. Significant modification of the MOKE spectra can be considered as a fingerprint of martensitic phase transition in Ni-Mn-Sn alloys.