Recycling polymer waste is a great challenge in the context of the growing use of plastics. Given the non-renewability of fossil fuels, the task of processing plastic waste into liquid fuels seems to be a promising one. Thermocatalytic conversion is one of the methods that allows obtaining liquid products of the required hydrocarbon range. Clays and clay minerals can be distinguished among possible environmentally friendly, cheap, and common catalysts. The moderate acidity and the presence of both Lewis and Brønsted acid sites on the surface of clays favor heavier hydrocarbons in liquid products of reactions occurring in their pores. Liquids produced with the use of clays are often reported as being in the gasoline and diesel range. In this review, the comprehensive information on the thermocatalytic conversion of plastics over clays obtained during the last two decades was summarized. The main experimental parameters for catalytic conversion of plastics according to the articles’ analysis, were the reaction temperature, the acidity of modified catalysts, and the catalyst-to-plastic ratio. The best clay catalysts observed were the following: bentonite/spent fluid cracking catalyst for high-density polyethylene (HDPE); acid-restructured montmorillonite for medium-density polyethylene (MDPE); neat kaolin powder for low-density polyethylene (LDPE); Ni/acid-washed bentonite clay for polypropylene (PP); neat kaolin for polystyrene (PS); Fe-restructured natural clay for a mixture of polyethylene, PP, PS, polyvinyl chloride (PVC), and polyethylene terephthalate (PET). The main problem in using natural clays and clay minerals as catalysts is their heterogeneous composition, which can vary even within the same deposit. The serpentine group is of interest in studying its catalytic properties as fairly common clay minerals.