Plastics play a vital role in modern society, but their accumulation in landfills and the environment presents significant risks to ecosystems and human health. In addition, the discarding of plastic waste constitutes to a loss of valuable material. While the usual mechanical recycling method often results in reduced material quality, chemical recycling offers exciting opportunities to valorize plastic waste into compounds of interest. Its versatility leans on the broad horizon of chemical reactions applicable, such as hydrogenolysis, hydrolysis, alcoholysis, or aminolysis. The development of heterogeneous and supported organocatalysts has enormous potential to enhance the economic and industrial viability of these technologies, reducing the cost of the process and mitigating its global environmental impact. This review summarizes the challenges and opportunities of chemically recycling heteroatom-containing plastics through heterogeneous catalysis, covering widely used plastics such as polyesters (notably PET and PLA), BPA-polycarbonate (BPA-PC), polyurethane (PU), polyamide (PA), and polyether. It examines the potential and limitations of various solid catalysts, including clays, zeolites, and metal–organic frameworks as well as supported organocatalysts and immobilized enzymes (heterogeneous biocatalysts), for reactions that facilitate the recovery of high-value products. By reintroducing these high-value products into the economy as precursors, this approach supports a more sustainable lifecycle for plastics, aligning with the principles of a circular economy.