My goal is to understand human verbal route instructions by modeling and implementing the language, knowledge representation, and cognitive processes needed to communicate about spatial routes. To understand human route instructions, I ran a study of how people give and follow route instructions. I modeled the language used in the route instruction texts using standard computational linguistics techniques. I model the information content of the route instruction texts using a spatial ontology. I introduce a set of axioms and heuristics that can autonomously transform a linguistic representation of what the route director said into a semantic representation of the intended route. This semantic representation has been implemented in mobile robots that can navigate and accomplish simultaneous localization and mapping in real- world environments. Finally, I model the processes of following and giving route instructions as Markov processes.