Advanced driver assistance systems (ADASs) are becoming increasingly common in modern-day vehicles, as they not only improve safety and reduce accidents but also aid in smoother and easier driving. ADASs rely on a variety of sensors such as cameras, radars, lidars, and a combination of sensors, to perceive their surroundings and identify and track objects on the road. The key components of ADASs are object detection, recognition, and tracking algorithms that allow vehicles to identify and track other objects on the road, such as other vehicles, pedestrians, cyclists, obstacles, traffic signs, traffic lights, etc. This information is then used to warn the driver of potential hazards or used by the ADAS itself to take corrective actions to avoid an accident. This paper provides a review of prominent state-of-the-art object detection, recognition, and tracking algorithms used in different functionalities of ADASs. The paper begins by introducing the history and fundamentals of ADASs followed by reviewing recent trends in various ADAS algorithms and their functionalities, along with the datasets employed. The paper concludes by discussing the future of object detection, recognition, and tracking algorithms for ADASs. The paper also discusses the need for more research on object detection, recognition, and tracking in challenging environments, such as those with low visibility or high traffic density.