Spintronic technology utilises the spin of electrons as an extra degree of freedom to store and process information in microelectronic devices. Of special interest among all spintronic materials are topological insulators (TIs), which have insulating bulk but conductive surface states. In this thesis, a comprehensive study of various TI and non-TI spintronic systems is presented, with an emphasis on the magneto-optic Kerr effect (MOKE) characterisation. The design and construction of a MOKE microscope is described, for simultaneous magneto-optical and magneto-transport measurements in an applied field of up to 9 T at temperatures from 1.5 to 300 K. This microscope is used to study Cr:Sb$2$Te$3$, (Cr,V):Sb$2$Te$3$, EuS/Bi$2$Se$3$, and [Cr:Sb$2$Te$3$/Dy:Bi$2$Te$3$]$\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}$ magnetic TI thin films. A good agreement is established between the electrical transport and MOKE results of the Cr:Sb$2$Te$3$ films. However, in (Cr,V):Sb$2$Te$3$, a discrepancy is found between the two measurement techniques, indicating the presence of the Cr$2$Te$3$ secondary phase in the sample. For EuS/Bi$2$Se$3,$ its interface-induced perpendicular magnetisation is successfully verified using the MOKE microscope. Regarding the ferromagnet/paramagnet [Cr:Sb$2$Te$3$/Dy:Bi$2$Te$3$]$\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}$ superlattice film, unexpected exchange bias is observed in the material with an exchange field of up to 0.15 T at 10 K. This finding is supported by a density-functional-theory calculation. Apart from TIs, several ferromagnet/semiconductor heterostructures are investigated for spin transport experiments, including $L10$-FePt/MgO/GaAs and [Co/Pt]/GaAs. None of them show promising magnetisation features for the further pursuit of spin injection into semiconductors. Finally, the surface science of a few magnetic and non-magnetic materials is investigated using low energy electron microscopy (LEEM). A new approach is established to de-oxidise the surface of W(110) substrates at 1800 K, a temperature considerably lower than in the standard W(110) cleaning procedure (2100 K). LEEM also reveals the high-temperature dynamics of the Pt-Si alloy on Si(100) substrates. Following the temperature increment, the Pt-Si alloy goes through the phases of nanowires, islands, and eutectic droplets. This research paves the way towards the future energy-efficient spintronic devices.