Vapor-phase material infiltration in polymer templates is an emerging material synthesis and patterning technique derived from atomic layer deposition, where gaseous organometallic precursors infiltrate polymer and react to form target inorganic material within organic matrix. This enables not only the synthesis of inorganic-organic hybrids with enhanced physical properties but also a direct patterning of inorganic nanostructures. In this talk, I will showcase our recent efforts on utilizing the method for patterning functioning metal oxide nanostructures based on self-assembled diblock copolymers (BCP) as well as lithographically-defined polymer templates. Particularly, we control precursor-BCP interaction and generate tone-reversed ZnO nanopatterns. Also demonstrated are metal oxide nanostructures with sub-40 nm linewidths, >15 aspect ratios, and three-dimensional morphologies, difficult to achieve by conventional nanofabrication procedures. Finally, one of the potential applications of the technique in a high-throughput fabrication of functional electrical devices is highlighted by patterning and characterizing polycrystalline in-plane ZnO nanowire field-effect transistor arrays.