A combination of block copolymer (BCP) lithography and solid-phase epitaxy can be employed to form large areas, on the order of square centimeters, of a high density of epitaxial crystalline complex oxide nanostructures. We have used BCP lithography with a poly(styrene-block-methyl methacrylate) (PS-b-PMMA) copolymer to template a nanohole array either directly on an (001)-oriented SrTiO3 (STO) single crystal substrate or on a 20 nm-thick Si3N4 layer deposited on the STO substrate. BCPs with the selected compositions assembled in a cylindrical phase with 16 nm diameter PMMA cylinders and a cylinder-to-cylinder spacing of 32 nm. The substrate was modified with an energetically non-preferential polymer layer to allow for the vertical alignment of the cylinders. The PMMA cylinders were removed using a subtractive process, leaving an array of cylindrical holes. For BCPs assembled on Si3N4/STO, the pattern was transferred to the Si3N4 layer using reactive ion etching, exposing the underlying STO substrate in the nanoholes. An amorphous LaAlO3 (LAO) layer was deposited on the patterned Si3N4/STO at room temperature. The amorphous LAO epitaxially crystallized within the nanoscale-patterned holes with fully relaxed lattice parameters through solid phase epitaxy, resulting in the formation of nanoscale LAO/STO epitaxial heterostructures.