The abundance of waste plastic is a major issue for the sustainability of the environment as plastic pollutes rivers, land, and oceans. However, the versatile behavior of plastic (it is lightweight, flexible, strong, moisture-resistant, and cheap) can make it a replacement for or alternative to many existing composite materials like concrete. Over the past few decades, many researchers have used waste plastic as a replacement for aggregates in concrete. This paper presents a comprehensive review of the engineering properties of waste recycled plastic. It is divided into three sections, along with an introduction and conclusion. The influence of recycled waste plastics on the fresh properties of concrete is discussed first, followed by its influence on the mechanical and durability properties of concrete. Current experimental results have shown that the mechanical and durability properties of concrete are altered due to the inclusion of plastic. However, such concrete still fulfills the requirements of many engineering applications. This review also advocates further study of possible pre-treatment of waste plastic properties for the modification of its surface, shape, and size in order to improve the quality of the composite product and make its use more widespread.