The surface-specific technique of vibrational sum frequency spectroscopy (VSFS) can provide vibrational information about chemical bonds at surfaces and interfaces. Two photons, of visible and infrared frequency, are spatially and temporally overlapped at a surface/interface to produce a photon at the sum frequency (SF) of the two input photons. As well as this process only being allowed in non-centrosymmetric media (i.e. VSFS is surface/interface specific), the SF process is enhanced when the IR beam is resonant with vibrational resonances. Broadband VSFS has been used in this project to study surfaces of two distinct classes of materials, namely graphene and polymers.Firstly, broadband VSFS was used to investigate the heating polymeric thin films using a home-built heated sample cell. The cell was tested using self-assembled monolayers (SAMs) of 1-octadecanethiol (ODT) grown on gold substrates. It was subsequently used to investigate thin films of poly(methyl methacrylate) (PMMA) of four different thicknesses and two different molecular weights that were spin-coated onto gold substrates. It was shown that the monolayers of ODT become disordered upon heating and solidified to incorporate the disorder introduced by the heating process. The PMMA films were also shown to become more disordered as a function of temperature.Secondly, broadband VSFS was used to investigate modified graphene, motivated by the fact that modifications to pristine graphene, be it intentional (i.e. functionalisation) or unintentional (i.e. contamination), cause the properties of graphene to change. This project focused on studying hydrogenated graphene, N-methylbenzamide functionalised graphene and contamination on commercial graphene. A method for calculating the number of hydrogen atoms in a hydrogen island was developed. VSF spectra of CH stretches in N-methylbenzamide functionalised graphene were obtained. Residues on commercially bought graphene were detected using VSFS and RAIRS. These residues were assigned to PMMA that remained on the CVD graphene by the process of transferring the CVD graphene from the copper foil on which it was grown onto the gold substrates.