Today, the scientific community is facing crucial challenges in delivering a healthier world for future generations. Among these, the quest for circular and sustainable approaches for plastic recycling is one of the most demanding for several reasons. Indeed, the massive use of plastic materials over the last century has generated large amounts of long-lasting waste, which, for much time, has not been object of adequate recovery and disposal politics. Most of this waste is generated by packaging materials. Nevertheless, in the last decade, a new trend imposed by environmental concerns brought this topic under the magnifying glass, as testified by the increasing number of related publications. Several methods have been proposed for the recycling of polymeric plastic materials based on chemical or mechanical methods. A panorama of the most promising studies related to the recycling of polyethylene (PE), polypropylene (PP), polyethylene terephthalate (PET), and polystyrene (PS) is given within this review.