A transparent conductive structure useful in the fabrication of electrical, electronic, and optoelectronic devices is provided by a mesh-like metallic structure in the form of a thin film having a plurality of apertures, e.g. one having an average size of 250 nm to 425 nm as measured in the largest dimension and an average nearest-neighbor spacing of 300 nm to 450 nm. In another aspect, the metallic thin film has plural sublayers of different metals, and may have apertures up to 2 μm in size and an average nearest-neighbor spacing of up to 2.5 μm. The metallic thin film may be 20 to 200 nm thick, and may be formed on a flexible or rigid substrate or on a device itself. The structure exhibits a transparency enhanced over a value determined simply by the fraction of the area of the metallic film occupied by the apertures.