Abstarct: Zinc oxide (ZnO), with a combination of II-VI elements, considered as a direct wide band gap (3.37 eV) semiconductor. This feature is very important not only in electronic device, like field effect transistors, but also in optoelectronic devices, such as light emitting diodes, blue and purple diode lasers and light detectors, as well. Using this material in these devices it is required to prepare the grown material in single crystalline condition, which is still an issue in the international community. Here in this thesis, we have first tried to explain theoretically the reported experimental data related to electrical transport properties of bulk pure and doped (ZnO:P) grown samples by various methods. Moreover, we have also tried to analyze the reported experimental data related to electrical transport properties in ZnMnO/ZnO and ZnMgO/ZnO heterostructures. In this section we have explored the reasons behind the electrical properties of the two dimensional electron gas (2DEG) formed in these nano-structures. It is notable that the former structure due to its low magnesium content, behaving as dilute magnetic semiconductor, is useful in both the electronic and magnetic applications, and the latter structure considering its high electron mobility is useful in High Mobility Electron Transistors (HMTs). Finally, we have investigated the electrical properties (the I-V characteristics) of thin film and nanowire ZnO field effect transistors. In this study the effect of mono-laxyer and multi-laxyer dielectrics and also the thickness of the gate dielectric are investigated. In this investigation, depending on the geometrical dimensions of the conducting channel, long and short channel effects are considered.