The dynamic aperture experiment at the CERN Super Proton Synchrotron (SPS) was aimed at finding the relevant effects that limit single-particle stability in hadron storage rings. These effects were studied in the SPS and compared with long-term particle tracking to determine to what extent computer simulations can predict the dynamic aperture under well-known conditions. Such investigations are very important for future hadron colliders such as the Large Hadron Collider as the design of these machines relies heavily on simulations. Besides this practical goal it was of utmost interest to improve the phenomenological understanding of the intricate details of particle motion in phase space. This experiment was carried out by successive teams over a period of ten years. We summarize the techniques, results, and conclusions.