Environmental studies have been concerned about the growth of plastic pollution in different ecosystems during the last decades, trying to raise awareness of the current and near-long-term situation. That is why different researchers have proposed the reuse of solid plastic waste, reincorporating it as a material within the construction area, using it as an “aggregate” in concrete mixtures for different types of uses that it provides, being one of the materials most used in the construction industry. The work presents the differences in how to reuse different types of recycled plastics as material/aggregate in concrete production, the experiments to which different samples were subjected, and their results. This paper is divided into five sections. The first section consists of a brief presentation of the types of plastics, their uses, and how they have been used in experiments in different laboratory tests. The following two sections address the properties provided by the use of recycled plastic in concrete mixtures in both fresh and hardened states. The fourth section focuses on the existing approaches in patents within the same topic, which are annexed. Then, we move on to the fifth section, discussing the contradictions and implications of producing concrete with recycled plastic.