The escalating environmental concerns associated with conventional plastic packaging have accelerated the development of sustainable alternatives, making food packaging a focus area for innovation. Bioplastics, particularly polyhydroxyalkanoates (PHAs), have emerged as potential candidates due to their biobased origin, biodegradability, and biocompatibility. PHAs stand out for their good mechanical and medium gas permeability properties, making them promising materials for food packaging applications. In parallel, zinc oxide (ZnO) nanoparticles (NPs) have gained attention for their antimicrobial properties and ability to enhance the mechanical and barrier properties of (bio)polymers. This review aims to provide a comprehensive introduction to the research on PHA/ZnO nanocomposites. It starts with the importance and current challenges of food packaging, followed by a discussion on the opportunities of bioplastics and PHAs. Next, the synthesis, properties, and application areas of ZnO NPs are discussed to introduce their potential use in (bio)plastic food packaging. Early research on PHA/ZnO nanocomposites has focused on solvent-assisted production methods, whereas novel technologies can offer additional possibilities with regard to industrial upscaling, safer or cheaper processing, or more specific incorporation of ZnO NPs in the matrix or on the surface of PHA films or fibers. Here, the use of solvent casting, melt processing, electrospinning, centrifugal fiber spinning, miniemulsion encapsulation, and ultrasonic spray coating to produce PHA/ZnO nanocomposites is explained. Finally, an overview is given of the reported effects of ZnO NP incorporation on thermal, mechanical, gas barrier, UV barrier, and antimicrobial properties in ZnO nanocomposites based on poly(3-hydroxybutyrate), poly(3-hydroxybutyrate-co-3-hydroxyvalerate), and poly(3-hydroxybutyrate-co-3-hydroxyhexanoate). We conclude that the functionality of PHA materials can be improved by optimizing the ZnO incorporation process and the complex interplay between intrinsic ZnO NP properties, dispersion quality, matrix–filler interactions, and crystallinity. Further research regarding the antimicrobial efficiency and potential migration of ZnO NPs in food (simulants) and the End-of-Life will determine the market potential of PHA/ZnO nanocomposites as active packaging material.