We report synthesis of some binary and ternary metal oxide nanostructures using microwave irradiation-assisted chemical synthesis, either in the presence or absence of a surfactant/structure directing agent. The method is simple, inexpensive, and yields nanoparticles of desired metal oxides in minutes, and requires no conventional templating. Nanoparticles of some functionally advanced binary/ternary metal oxides (MnO2, ZnO, CuO, ZnMn2O4 etc) have been synthesized using metal acetylacetonates as the starting precursor material and microwave as the source of energy, in a process developed in detail in our laboratory. The nanoparticle size varies from 7-50 nm. Emphasis has been placed on the synthesis of ZnO nanostructures, particularly ZnO nanoshells, which do not require any surfactant/structure-directing agent for synthesis. There is a systematic variation in the morphology of the ZnO nanostructures with variation of process parameters, such as microwave power, microwave irradiation time, type of solvents, surfactants/structure-directing agents and its type and concentration. The as-prepared powder sample may either need a very brief exposure to heat to remove the surfactant or no post-synthesis processing, and is found to be well-crystallised. Determination of their crystallinity, actual shape, and orientation was made using X-ray diffraction, scanning electron microscopy (SEM) and transmission electron microscopy (TEM).