Amorphous oxide semiconductors (AOSs)--ternary or quaternary oxides of post-transition metals such as In-Sn-O, Zn-Sn-O, or In-Ga-Zn-O–have been known for a decade and have attracted a great deal of attention as they possess several technological advantages, including low-temperature large-area deposition, mechanical flexibility, smooth surfaces, and high carrier mobility that is an order of magnitude larger than that of amorphous silicon (a-Si:H). Compared to their crystalline counterparts, the structure of AOSs is extremely sensitive to deposition conditions, stoichiometry, and composition, giving rise to a wide range of tunable optical and electrical properties. The large parameter space and the resulting complex deposition--structure--property relationships in AOSs make the currently available theoretical and experimental research data rather scattered and the design of new materials difficult. In this work, the key properties of several In-based AOSs are studied as a function of cooling rates, oxygen stoichiometry, cation composition, or lattice strain. Based on a thorough comparison of the results of ab initio modeling, comprehensive structural analysis, accurate property calculations, and systematic experimental measurements, a four-dimensional parameter space for AOSs is derived, serving as a solid foundation for property optimization in known AOSs and for design of next-generation transparent amorphous semiconductors.