With the isolation and characterisation of graphene in 2004 there came a revolution in the field of solid state physics. As new atomically thin materials were identified and isolated, a wide range of optical, electrical and mechanical properties became apparent suggesting that such materials could be used in innovative technologies. In this thesis, the optical and electronic properties of three different two-dimensional materials are investigated. These are: atomically thin semiconductors from the family of transition metal dichalcogenides (TMDs); graphene; and, finally, layered organic/inorganic perovskites. More specifically, a study of CVD-grown TMD WS₂ highlights the dependence of the electrical properties on different growth precursors, and it identifies the best synthesis conditions to attain a record-high charge carrier mobility. At the same time, an investigation of the electrical characteristics of graphene and a metal-halide perovskite explores the electrical properties at large electric fields. For the perovskite, an unusual non-monotonous electric field dependence of the longitudinal current density is observed where, unlike for graphene and silicon, no current saturation occurs. This behaviour is attributed to intra-band scattering of the charge carriers and in future could be used to determine the mechanisms of charge carrier transport in this material and similar perovskites. Further studies of the same perovskite at low values of electric field demonstrate the suitability of this layered system for developing fast and highly sensitive photodetectors. Devices made using pre-patterned substrates exhibit excellent peak responsivity R = 7835 AW¯¹, ultra-fast response times of 6 ns, very high peak detectivity D* = 5.45x10²¹ Jones and a linear dynamic range of 211 dB. These devices also perform successfully when fabricated on flexible substrates.