The main goal of this review paper was to study the physical and chemical properties of agricultural crop wastes and their potentials to partially replace in production of mortar and concrete. Bamboo leaves’ ashes (BLA), banana leaves’ ashes (BNLA), corncob leaves’ ashes (CCA), groundnut ashes (GNA), rice husk ashes (RHA), and sugarcane bagasse ashes (SCBA) were selected to be reviewed. The chemical composition of these agricultural wastes revealed that the they are basically composed of alumino-siliceous materials conforming the requirement of pozzolanic materials. Compared with cement, they have finer particle size and higher surface area. The effect of partial replacement of cement by BLA, BNLA, CCA, GNA, RHA, and SCBA on the properties of fresh concrete (consistency, workability, and setting time), mechanical properties (compressive and tensile strength), microstructure (scanning electron microscopy, derivative thermogravimetry, and X-ray diffraction), and durability (ultrapulse velocity, water absorption, and sulphate attack) of concrete was recapped. The inclusion of BLA, CCA, RHA, and SCBA as partial replacement of cement reduced the workability of concrete due to their finer particle size. The mechanical performance of concrete showed enhancement with partial replacement of cement by BLA, RHA, and SCBA due to the involvement of amorphous silica in secondary reaction to produce densified tetrahedral gel. Consequently, uniform and denser morphology was formed, and durability was enhanced as densification of hydrated gel increased. In general, the review exposed that agricultural crop wastes satisfy pozzolanic material properties and have strong potential to replace cement up to 10% without compromising the performance of concrete.