This thesis focuses on the synthesis and characterisation of two materials, monolayer molybdenum disulphide (MoS2) crystals and gold nanocrystals/monolayers, supported on single crystal strontium titanate (SrTiO3) substrates. On three terminations of SrTiO3 substrates, (111), (110), and (001), monolayer MoS2 crystals are found to preferentially align their -type directions (i.e., the sulphur-terminated edge directions) with the -type directions on SrTiO3. These arrangements allow near-perfect coincidence epitaxy between seven MoS2 unit cells and four SrTiO3 unit cells. This maximises the interfacial van der Waals bonding between MoS2 monolayers and SrTiO3. When SrTiO3-supported MoS2 monolayers are annealed in ultrahigh vacuum, the sulphur loss begins at 700 °C. The sulphur vacancies can be filled by annealing the crystals in a hot sulphur atmosphere, and the optical properties of monolayer MoS2 can nearly be fully recovered. The sulphur annealing no longer takes effect when all the Mo has been oxidised into MoO2 and MoO3 at 800–900 °C. The MoS2 crystal shapes are stable upon annealing until the residual MoO3 particles evaporate at above 1000 °C. Gold nucleates as monolayers on SrTiO3(001)-(2 × 1) and as multiply twinned particles on SrTiO3(001)-c(4 × 2) and SrTiO3(111)-(4 × 4)+(6 × 6). In scanning tunnelling microscopy, a square pattern of bright spots with a periodicity of 1.54 ± 0.06 nm is frequently observed. The monolayers are thought to adopt mixed hexagonal and square packing of atoms because of their observed internal angles of 60°/120° and 90°/135°. The shapes of gold nanocrystals deviate from the equilibrium Wulff shape due to the influence of the SrTiO3 single crystal substrates. On any SrTiO3 substrate, the height-to-width ratio of gold crystals is not a constant but rather increases the crystal height. The ratio between the {111} and {001} surface areas of the gold crystals is found to differ on three different SrTiO3 substrates. The reentrant facets of the Wulff shapes are not observed. These findings extend our understanding of epitaxial crystals and nanomaterials grown on SrTiO3. This yields a platform for the growth of tailored nanomaterials for electronic and catalytic applications.