CuI is a p-type transparent conductive semiconductor with unique optoelectronic properties, including wide band gap (3.1 eV), high hole mobility (>40 cm2 V−1 s−1 in bulk), and large room-temperature exciton binding energy (62 meV). The difficulty in epitaxy of CuI is the main obstacle for its application in advanced solid-state electronic devices. Herein, room-temperature heteroepitaxial growth of CuI on various substrates with well-defined in-plane epitaxial relations is realized by reactive sputtering technique. In such heteroepitaxial growth the formation of rotation domains is observed and hereby systematically investigated in accordance with existing theoretical study of domain-epitaxy. The controllable epitaxy of CuI thin films allows for the combination of p-type CuI with suitable n-type semiconductors with the purpose to fabricate epitaxial thin film heterojunctions. Such heterostructures have superior properties to structures without or with weakly ordered in-plane orientation. The obtained epitaxial thin film heterojunction of p-CuI(111)/n-ZnO(00.1) exhibits a high rectification up to 2 × 109 (±2 V), a 100-fold improvement compared to diodes with disordered interfaces. Also a low saturation current density down to 5 × 10−9 Acm−2 is formed. These results prove the great potential of epitaxial CuI as a promising p-type optoelectronic material.