In this review, we provide an overview of emerging trends and challenges in the field of intelligent and autonomous, or self-driving, vehicles. Recent advances in the field of perception, planning, and decision-making for autonomous vehicles have led to great improvements in functional capabilities, with several prototypes already driving on our roads and streets. Yet challenges remain regarding guaranteed performance and safety under all driving circumstances. For instance, planning methods that provide safe and system-compliant performance in complex, cluttered environments while modeling the uncertain interaction with other traffic participants are required. Furthermore, new paradigms, such as interactive planning and end-to-end learning, open up questions regarding safety and reliability that need to be addressed. In this survey, we emphasize recent approaches for integrated perception and planning and for behavior-aware planning, many of which rely on machine learning. This raises the question of verification and safety, which we also touch upon. Finally, we discuss the state of the art and remaining challenges for managing fleets of autonomous vehicles.