Continual advancements in the development of synchrotron radiation sources have resulted in X-ray based spectroscopic techniques capable of probing the electronic and structural properties of numerous systems. This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as K resonant inelastic X-ray scattering (RIXS), to the study of electronic structure in transition metal sites with emphasis on experimentally quantifying 3d orbital covalency. The specific sensitivities of K-edge XAS, L-edge XAS, and RIXS are discussed emphasizing the complementary nature of the methods. L-edge XAS and RIXS are sensitive to mixing between 3d orbitals and ligand valence orbitals, and to the differential orbital covalency (DOC), that is, the difference in the covalencies for different symmetry sets of the d orbitals. Both L-edge XAS and RIXS are highly sensitive to and enable separation of and donor bonding and back bonding contributions to bonding. Applying ligand field multiplet simulations, including charge transfer via valence bond configuration interactions, DOC can be obtained for direct comparison with density functional theory calculations and to understand chemical trends. The application of RIXS as a probe of frontier molecular orbitals in a heme enzyme demonstrates the potential of this method for the study of metal sites in highly covalent coordination sites in bioinorganic chemistry.