For next-generation smart cities, small UAVs (also known as drones) are vital to incorporate in airspace for advancing the transportation systems. This paper presents a review of recent developments in relation to the application of UAVs in three major domains of transportation, namely; road safety, traffic monitoring and highway infrastructure management. Advances in computer vision algorithms to extract key features from UAV acquired videos and images are discussed along with the discussion on improvements made in traffic flow analysis methods, risk assessment and assistance in accident investigation and damage assessments for bridges and pavements. Additionally, barriers associated with the wide-scale deployment of UAVs technology are identified and countermeasures to overcome these barriers are discussed, along with their implications.