This study presents a comprehensive literature survey on facility location problems for drone (uncrewed vehicle) delivery in situations where drones can ride in or on other vehicles. This includes facilities visited by only one type of vehicle, as well as facilities visited by both drones and other vehicles. Unlike traditional facility location problems for delivery systems with one vehicle type, hybrid vehicle-drone delivery systems usually require determining locations where the two vehicle types meet and separate. The main goals of this paper are to review the large volume of drone delivery literature with riding from a facility location perspective to provide a connection between the studies from different research areas that cover similar problems, and to highlight future research directions in this area. We first review the functions of drones, including aerial and ground drones, and the different types of facilities used for hybrid vehicle-drone delivery systems. The literature is categorized based on the presence of resupply operations, the locations of drone launch and retrieval points, the types of drones (aerial or ground) and the location space (discrete or continuous). Each category is analyzed in terms of the modeling approach, decision(s), objective function(s), constraints and additional features. The paper concludes with promising future research directions. •Facility location research for drone delivery with riding is reviewed.•Facility functions and types for drone delivery with riding are classified.•Over 160 studies are reviewed and classified.•Most studies consider time objectives using single-delivery UAV trips.•Promising future research directions are identified.