A primary concern of conventional Portland cement concrete (PCC) is associated with the massive amount of global cement and natural coarse aggregates (NCA) consumption, which causes depletion of natural resources on the one hand and ecological problems on the other. As a result, the concept of green concrete (GC), by replacing cement with supplementary cementitious materials (SCMs) such as ground granulated blast furnace slag (GGBFS), fly ash (FA), silica fume (SF), and metakaolin (MK), or replacing NCA with recycled coarse aggregates, can play an essential role in addressing the environmental threat of PCC. Currently, there is a growing body of literature that emphasizes the importance of implementing GC in concrete applications. Therefore, this paper has conducted a systematic literature review through the peer-reviewed literature database Scopus. A total of 114 papers were reviewed that cover the following areas: (1) sustainability benefits of GC, (2) mechanical behavior of GC in terms of compressive strength, (3) durability properties of GC under several environmental exposures, (4) structural performance of GC in large-scale reinforced beams under shear and flexure, and (5) analytical investigation that compares the GC shear capacities of previously tested beams with major design codes and proposed models. Based on this review, the reader will be able to select the optimum replacement level of cement with one of the SCMs to achieve a certain concrete strength range that would suit a certain concrete application. Also, the analysis of durability performance revealed that the addition of SCMs is not recommended in concrete exposed to a higher temperature than 400 °C. Moreover, combining GGBFS with FA in a concrete mix was noticed to be superior to PCC in terms of long-term resistance to sulfate attack. The single most striking observation to emerge from the data comparison of the experimentally tested beams with the available concrete shear design equations is that the beams having up to 70% of FA as a replacement to OPC or up to 100% of RCA as a replacement to NCA were conservatively predicted by the equations of Japan Society of Civil Engineers (JSCE-1997), the American Concrete Institute (ACI 318-19), and the Canadian Standards Association (CSA-A23.3-14).