For nanoscale materials, the electronic, including optical, properties of a system are highly influenced by the effects of spin-orbit coupling (SOC). These SOC effects include defining a systems overall spin character, generating zero-field energy splittings (ZFS) between states, and form the basis for spectroscopic selection rules. The quantification of electronic structures parameters related to SOC such as Landé g-factors and ZFS energies can provide a deep understanding of the optical properties of a system. Magneto-optical (MO) techniques such as magnetic circular dichroism (MCD) and, more recently, magnetic circular photoluminescence (MCPL) spectroscopies have been used to dissect SOC and electronic structure of systems ranging from metalloenzymatic proteins to semiconductor quantum dots. The goal of this chapter is to introduce the reader to the fundamentals of MO spectroscopy geared toward the study of nanoscale materials. This includes deriving the underlying principles of MCD and MCPL methods. A case study is presented using the Au₂₅(PET)₁₈ monolayer-protected nanocluster as a model system. Results from VTVH-MCPL measurements on the Au₂₅(PET)₁₈ nanocluster serve to demonstrate how magneto-optical spectroscopy methods can characterize the optical properties of nanoscale through quantification of electronic structure parameters such as Landé g-factors, ZFS energies, and Faraday terms.