This thesis is about the growth of ZnO thin films for optoelectronic applications. ZnO thin films were grown using plasma assisted molecular beam epitaxy and were studied using various conventional and novel characterisation techniques. The significance of different growth variables on growth efficiency was investigated. The growth rate of ZnO films was found to be linearly dependent on the Zn flux under O-rich growth conditions. Under Zn-rich conditions, the growth rate was dependent on both atomic and molecular oxygen flux. By characterising the oxygen plasma generated using different RF power and aperture plate designs and correlating the results with the growth rates observed, it was found that atomic oxygen was the dominant growth species under all conditions. Molecular oxygen also participated in the growth process, with its importance dependent on the aperture plate design. In addition, an increase in growth temperature was found to monotonically decrease the growth rate. A growth rate of 1.4 Å/s was achieved at a growth temperature of 650 ℃ by using an oxygen flow rate of 1.6 standard cubic centimetres utilising a plasma source with a 276 hole plate operating at 400 W, and a Zn flux 1.4✕10¹⁵ atoms/cm²⋅s. Characterisation of the MBE grown thin films revealed that the qualities of ZnO thin films were dependent on the growth conditions. Experimental evidence suggested that a maximum adatom diffusion rate can be achieved under Zn-rich conditions, giving samples with the best structural quality. O-rich conditions in general led to statistical roughening which resulted in rough and irregular film surfaces. Experimental results also suggested that by increasing the atomic oxygen content and decreasing the ion content of the plasma, the excitonic emission of the ZnO thin films can possibly be improved. It was also found that the conductivity of the films can possibly be reduced by increasing the plasma ion content. By investigating the evolution of the buffer layer surface during the early stages of growth, dislocation nucleation and surface roughening were found to be important strain relief mechanisms in MBE grown ZnO thin films that affected the crystal quality. The usage of LT-buffer layers was found to improve substrate wetting, and was shown to significantly reduce dislocation propagation. Further strain reduction was achieved via the application of a 1 nm MgO buffer layer, and a significant reduction of carrier concentration and improvement in optical quality was subsequently observed. A carrier concentration of <1✕10¹⁶ cm⁻³ and a near band emission full width half maximum of 2 meV was observed for the best sample. The study of electrical characteristics using the variable magnetic field Hall effect confirmed the existence of a degenerate carrier and a bulk carrier in most MBE grown ZnO thin films. The bulk carrier mobility was measured to be ~120 - 150 cm²/Vs for most as-grown samples, comparable to the best reported value. A typical bulk carrier concentration of ~1✕10¹⁶ - 1✕10¹⁸ cm⁻³ was observed for as-grown samples. Annealing was found to increase the mobility of the bulk carrier to ~120 - 225 cm²/Vs and decrease the bulk carrier concentration by two orders of magnitude. Using time resolved photoluminescence, it was found that the radiative recombination in MBE grown ZnO thin films was dominated by excitonic processes, and followed a T³⁄² trend with temperature. A maximum radiative lifetime of 10 ns was observed for as-grown samples. The non-radiative lifetime in ZnO thin films was dominated by the Shockley-Read-Hall recombination processes. The modelling of the temperature dependence of the non-radiative lifetime suggested that an electron trap at ~0.065 eV and a hole trap at ~0.1 eV may be present in these samples. The application of time resolved photoluminescence also allowed the direct observation of carrier freeze-out in these ZnO films at low temperature.