With the increase in demand for plastic use, waste plastic (WP) management remains a challenge in the contemporary world due to the lack of sustainable efforts to tackle it. The increment in WPs is proportional to man’s demand and use of plastics, and these come along with environmental challenges. This increase in WPs, and the resulting environmental consequences are mainly due to the characteristic biodegradation properties of plastics. Landfilling, pollution, groundwater contamination, incineration, and blockage of drainages are common environmental challenges associated with WPs. The bulk of these WPs constitutes polyethene (PE), polyethene terephthalate (PET) and polystyrene (PS). Pyrolysis is an eco-friendly thermo-chemical waste plastic treatment solution for valuable product recovery, preferred over landfilling and incineration solutions. In this extensive review, a critical investigation on waste plastic catalytic pyrolysis (WPCP) is performed, including catalyst and non-catalyst applications to sustainably tackle WP management. Current catalysis techniques are revealed, and some comparisons are made where necessary. Common pyrolytic products and common shortcomings and errors related to WP catalysis were also identified. The benefits of catalysts and their applications to augment and optimise thermal pyrolysis are emphasised. With all these findings, and more, this paper provides reassurance on the significance of catalysis to industrial-scale applications and products and supports related WPCP research work concerning the environment and other beneficiaries.