Vision based mobile robot guidance has proven difficult for classical machine vision methods because of the diversity and real time constraints inherent in the task. This thesis describes a connectionist system called ALVINN (Autonomous Land Vehicle In a Neural Network) that overcomes these difficulties. ALVINN learns to guide mobile robots using the back-propagation training algorithm. Because of its ability to learn from example, ALVINN can adapt to new situations and therefore cope with the diversity of the autonomous navigation task. But real world problems like vision based mobile robot guidance presents a different set of challenges for the connectionist paradigm.