Using recycled aggregate (RA) and slag instead of natural aggregate (NA) and cement can reduce greenhouse gas emissions (GHGE) and achieve effective waste recovery. In recent years, RA has been widely used to replace NA in concrete. Every year, several researchers conduct investigations on the mechanical performance and durability of recycled aggregate concrete (RAC). Due to the loose and porous material properties of RA, the mechanical properties and durability of RAC, such as strength, carbonation resistance, permeability resistance and chloride ion penetration resistance, are greatly reduced compared with natural aggregate concrete. In contrast, concrete containing slag instead of NA and cement generally improved the strength of concrete and reduced the internal porosity of materials. Herein, we discuss the effects of RA and slag on the workability, compressive strength, splitting tensile strength, ultrasonic pulse velocity (UPV) value, and elastic modulus of concrete. The relationships between the compressive strength and the splitting tensile strength, UPV value, and elastic modulus are discussed, and the optimal substitution method is proposed. In addition, various equations for calculating the compressive strength of concrete based on performance factors related to the compressive strength are summarized.