There has been considerable recent interest in the design of diluted magnetic semiconductors, with a particular focus on the exploration of different semiconductor hosts. Among these, the oxide-based diluted magnetic semiconductors are attracting increasing attention, following reports of room temperature ferromagnetism in anatase TiO2 and wurtzite ZnO doped with a range of transition metal ions. In this review we summarize the current status of oxide-based diluted magnetic semiconductors, and discuss the influence of growth method, substrate choice, and temperature on the microstructure and subsequent magnetic properties of thin films. We outline the experimental conditions that promote large magnetization and high ferromagnetic Curie temperature. Finally, we review the proposed mechanisms for the experimentally observed ferromagnetism and compare the predictions to the range of available data.