This article provides an overview of plastic recycling development since the 1970s. It discusses the three common recycling options: mechanical recycling, chemical recycling, and energetic recycling. Additionally, it considers the challenges of waste cleaning and sorting. The article describes the mechanical and chemical recycling processes in detail for the main constituents of plastic waste, such as polyethylene (PE), polypropylene (PP), polystyrene (PS), polyvinyl chloride (PVC), and polyethylene terephthalate (PET). The current recycling rates indicate that only mechanical recycling is economically viable, which is insufficient for a sustainable circular economy. Chemical recycling methods are often too energy-intensive and require complex presorting making them unattractive. To become economically competitive, requirements for chemical recycling methods have been derived in this article. In this context, the splitting of polymer chains using low-temperature atmospheric pressure plasma is proposed as a novel technology. To date, this technology has only been used for the surface treatment of plastic. However, it shows the potential for processing unsorted, low-value plastic waste, especially PE, PP, and mixed waste, which would otherwise be sent for incineration or to landfills. Mechanical recycling is often unsuitable for these waste streams, and competitive chemical recycling methods are not yet established on an industrial scale.