This thesis presents experimental studies on the the tantalum and rhenium dichalcogenides (TaX
2 and ReX
2, respectively), both of which exhibit distorted structures described in terms of a Peierl’s transition of the crystal lattice. In the case of TaX
2, this distortion occurs as a transition from the high-temperature metallic phase to a charge-density-wave (CDW) state at low temperatures. On the other hand, the distorted structure of ReX
2 is known to be stable throughout its solid state. Here, the structural, optical and electrical properties of these distorted materials are studied using a number of experimental techniques. Firstly, TaX
2 samples have been grown using the chemical-vapour-transport method, producing bulk single crystals with large lateral dimensions. Crystals with mixed chalcogen compositions have been produced (TaS
2-xSe
x), with good control of stoichiometry. These crystals have been chemically analysed using X-ray photoemission and energy-dispersive X-ray spectroscopies. In particular, the alloy 1T-TaS
1.2Se
0.8 has been grown and then studied at a range of temperatures, wherein several CDW transitions are observed. This specific alloy displays marked hysteresis in its phase transitions during cooling and heating, which is evidenced in electrical transport, Raman spectroscopy and X-ray diffraction measurements. Additional photoemission measurements have allowed the electronic structure of the material to be studied. The unusual hysteresis observed in 1T-TaS
2-xSe
x is explained by considering the effect of substituting sulphur for selenium on the crystal structure, and the impact this has on the dynamics of the CDW phase transitions. Next, this thesis demonstrates the embedding of ReX
2 directly within photonic waveguides, for future nonlinear optical studies. This benefits from the distorted crystal structure of this material, which results in anisotropic in-plane properties. The micro-mechanical exfoliation of ReS
2 flakes is presented, in which the flakes are found to preferentially cleave along one in-plane crystallographic direction, producing flakes with high aspect ratios that are ideal for incorporation within waveguides. These flakes are characterised using atomic force microscopy and polarised Raman spectroscopy, of which the latter is demonstrated to provide a reliable means of identifying the in-plane orientation of ReS
2. Flakes fabricated and characterised by the author have subsequently been embedded within chalcogenide-glass waveguide structures by collaborators. To characterise these devices, an optical set-up was designed and constructed. The use of this set-up has been verified with a characterisation of blank waveguides, additionally showing the linear and nonlinear optical properties of chalcogenide glasses.