Polymeric wastes, specifically polyethylene terephthalate (PET) and scrap tyre rubber (STR), pose a significant environmental issue. PET, a thermoplastic polymer, is widely used in manufacturing bottles, PET cups, containers, fibres, films, and packaging materials. On the other hand, colossal rubber tyre waste quantities represent other environmental problems. However, PET and STR wastes are often discarded in the immediate vicinity, contributing to water resource pollution and landfill site strain. One solution is to replace aggregates in concrete mixtures with these wastes, a preferable alternative to landfill disposal because of the large volume and slow decomposition rate in landfills. Recycling PET and STR helps mitigate environmental pollution and promotes resource conservation and sustainability. This study aims to review previous research undertaken in the field and validate the findings of concrete’s fresh, mechanical, and functional characteristics. Based on the review, most studies confirmed a noticeable decline in the mechanical characteristics of mortar and concrete. However, these studies did not effectively focus on using PET and STR as sound and thermal insulation aggregates. Replacing PET and STR as aggregate in concrete can reduce thermal conductivity and acoustics.