The desire for developing ultraviolet optoelectronic devices has prompted extensive studies toward wide-bandgap semiconductor ZnO and its related alloys. Bandgap engineering as well as p-type doping is the key toward practical applications of ZnO. As yet, stable and reproducible p-type doping of ZnO remains a formidable challenge. To circumvent p-type conductivity, ZnO-based optoelectronic devices have been developed with hetero-structures of ZnO alloys. In past decades, substantial efforts have been made to engineer the band structure of ZnO via isovalent cation- or anion-substitution for obtaining desired material properties, and considerable progresses have been achieved. The purpose of this review is to summarize recent advances in the experimental and theoretical studies on bandgap engineering of ZnO by formation of multi-component alloys, and the development of related hetero-structures and optoelectronic devices. First, we briefly introduce the general properties, epitaxial growth techniques, and bandgap engineering of ZnO. Then, we focus on presenting the current status of researches on ZnO ternary and quaternary alloys for bandgap engineering. The issues about substituent solubility limit and phase separation, as well as variations of lattice parameters and bandgap with the substituent content in the alloys are discussed in detail. Further, ZnO alloys based hetero-structures including hetero-junctions, quantum wells, and superlattices are reviewed, and recent achievements in the area of optoelectronic devices based on ZnO multi-component alloys are summarized. The review closes with outlooking the likely developing trend of multi-component alloys for the bandgap engineering of ZnO and related hetero-structures, and the potential and pathway of multi-component alloys in settling the p-type doping of ZnO.