We present Scanning Tunneling Microscopy (STM) studies on several systems in which spin-orbit coupling leads to new and interesting physics, and where tuning by doping and/or strain can significantly modify the electronic properties, either inducing a phase transition or by sharply influencing the electronic structure locally. In the perovskite Iridate insulator Sr3Ir2O7, we investigate the parent compound, determining the band gap and its evolution in response to point defects which we identify as apical oxygen vacancies. We investigate the effects of doping the parent compound with La (in place of Sr) and Ru (in place of Ir). In both cases a metal-insulator transition (MIT) results: at x ~ 38% with Ru, and x ~ 5% with La. In the La-doped samples we find nanoscale phase separation at dopings just below the MIT, with metallic spectra associated with clusters of La atoms. Further, we find resonances near the Fermi energy associated with individual La atoms, suggesting an uneven distribution of dopants among the layers of the parent compound. Bi2Se3 is a topological insulator which hosts linearly dispersing Dirac surface states. Doping with In (in place of Bismuth) brings about topological phase transition, achieving a trivial insulator at x ~ 4%. We use high-magnetic field Landau level spectroscopy to study the surface state’s properties approaching the phase transition and find, by a careful analysis of the peak positions find behavior consistent with strong surface-state Zeeman effects: g~50. This interpretation implies, however, a relabeling of the Landau levels previously observed in pristine Bi2Se3, which we justify through ab initio calculations. The overall picture is of a g-factor which steadily decreases as In is added up to the topological phase transition. Finally, we examine the effects of strain on the surface states of (001) thin films of the topological crystalline insulator SnTe. When these films are grown on closely-related substrates—in this case PbSe(001)—a rich pattern of surface strain emerges. We use phase-sensitive analysis of atomic-resolution STM topographs to measure the strain locally, and spatially-resolved quasiparticle interference imaging to compare the Dirac point positions in regions with different types of strain, quantifying for the first time the effect of anisotropic strain on the surface states of a topological crystalline insulator.