In the near future, humans will be relieved from parking. Major improvements in autonomous driving allow the realization of automated valet parking (AVP). It enables the vehicle to drive to a parking spot and park itself. This paper presents a review of the intelligent vehicles literature on AVP. An overview and analysis of the core components of AVP such as the platforms, sensor setups, maps, localization, perception, environment model, and motion planning is provided. Leveraging the potential of AVP, high density parking (HDP) is reviewed as a future research direction with the capability to either reduce the necessary space for parking by up to 50% or increase the capacity of future parking facilities. Finally, a synthesized view discussing the remaining challenges in automated valet parking and the technological requirements for high density parking is given.