Concrete is a heterogeneous material that consists of cement, aggregates, and water as basic constituents. Several cementitious materials and additives are added with different volumetric ratios to improve the strength and durability requirements of concrete. Consequently, performance of concrete when exposed to elevated temperature is greatly affected by the concrete type. Moreover, post-fire properties of concrete are influenced by the constituents of each concrete type. Heating rate, days of curing, type of curing, cooling method, and constituents of the mix are some of the factors that impact the post-fire behavior of concrete structures. In this paper, an extensive review was conducted and focused on the effect of concrete constituents on the overall behavior of concrete when exposed to elevated temperature. It was evident that utilizing fibers can improve the tensile capacity of concrete after exposure to higher temperatures. However, there is an increased risk of spalling due to the induced internal stresses. In addition, supplementary cementitious materials such as metakaolin and silica fume enhanced concrete strength, the latter proving to be the most effective. In terms of the heating process, it was clear that several constituents, such as silica fume or fly ash, that decrease absorption affect overall workability, increase the compressive strength of concrete, and can yield an increase in the strength of concrete at 200 °C. Most of the concrete types show a moderate and steady decrease in the strength up until 400 °C. However, the decrease is more rapid until the concrete reaches 800 °C or 1000 °C at which it spalls or cannot take any applied load. This review highlighted the need for more research and codes’ provisions to account for different types of concrete constituents and advanced construction materials technology.