This paper discusses some of the current state-ofthe-art and remaining challenges in path planning and vehicle control for enabling autonomous vehicles. Reliable path planning is fundamental for the proper operation of an autonomous vehicle. Typically, the path planner relies on an incomplete model of the surroundings to generate a reference trajectory, used as input to a vehicle controller that tracks this reference trajectory. Depending on how much complexity is put into the path-planning block, the path planning and vehicle-control blocks can be viewed as independent of each other, connected to each other, or merged into one block. There are several types of path-planning techniques developed over the last decades, each with its own set of benefits and drawbacks. We review different techniques for path planning and trajectory generation, and give examples of its use in relation to autonomous vehicles. We report on our own recent findings and give an outlook on potential research directions.