Reinforced concrete structures and structural members used in strategic infrastructures such as highway bridges, high-rise buildings, etc. are inherently subjected to lateral impact loads arising from the collision of vehicles, vessels, falling rocks, and rigid objects having different impact geometries, weights, and velocities. Due to the brittle nature of concrete materials, both localized and overall failure modes are very likely to occur in concrete structures under dynamic and impulsive loads. Hence, many attempts have been carried out in the literature to recognize the failure behaviors and to assess the vulnerability of concrete structure under lateral impact loads. This paper presents a comprehensive state-of-the-art review on the responses and failure behaviors of various types of concrete structures and structural members subjected to lateral impact loads based on analytical, numerical, and experimental studies carried out by the previous research works. In addition, the influences of various structural- and load-related parameters on the impact resistance and failure behaviors of different concrete structures under lateral impact loads are reviewed.