A wide variety of insects use spatial memories in behaviours like holding a position in air or flowing water, in returning to a place of safety, and in foraging. The Hymenoptera, in particular, have evolved life-histories requiring reliable spatial memories to support the task of provisioning their young. Behavioural experiments, primarily on social bees and ants, reveal the mechanisms by which these memories are employed for guidance to spatial goals and suggest how the memories, and the processing streams that use them, may be organized. We discuss three types of memory-based guidance which, together, can explain a large part of observed insect spatial behaviour. Two of these, alignment image-matching and positional image-matching, are based on an insect's remembered views of its surroundings: The first uses views to keep to a familiar heading and the second to head towards a familiar place. The third type of guidance is based on a process of path integration by which an insect monitors its distance and direction from its nest through odometric and compass information. To a large degree, these guidance mechanisms appear to involve modular computational systems. We discuss the lack of evidence for cognitive maps in insects, and in particular the evidence against a map based on path integration, in which view-based and path integration memories might be combined. We suggest instead that insects have a collective of separate guidance systems, which cooperate and train each other, and together provide reliable guidance over a range of conditions.