Plastic packaging has gained an increasing amount of attention in all aspects of society. Over the past several decades, plastics became the material of choice due to their excellent properties, performance, and economics, but the end of life of plastics is not well managed. This has led to plastic waste in our environment, especially the oceans, rivers, and estuaries, driving legislative, industrial, and voluntary initiatives to make the necessary pivot to circularity. While the plastics recycling industry has made many advances in its relatively short life, there are still many technical and societal hurdles to be overcome. The goal of this work is not to provide a complete review of recycling as it pertains to circularity, but rather to highlight the technical gaps that need to be collaboratively addressed by the entire plastics community to achieve circularity. Each stage along the path, from design of packaging and materials of construction to sortation, recycling, and reprocessing are ripe for innovation. The most relevant issues are introduced to provide a starting point for research across all fields of polymer science to aid in reducing the environmental impact of plastic packaging waste.