This article covers methodological and theoretical issues in artificial grammar learning. Arguments that such tasks are mediated by abstract knowledge (e.g., A. S. Reber, 1969A. S. Reber, , 1990 are based primarily on evidence from transfer experiments, where the surface vocabulary is changed between learning and test items. Because of a number of methodological concerns, the small magnitudes of artificial grammar leaming effects generally are difficult to interpret. Possible solutions are offered here. Furthermore, even reliable transfer effects imply neither that subjects have acquired abstract knowledge of the underlying grammar nor that they are performing a process of abstract analogy from memorized whole exemplars. Models that learn only surface fragments of the training stimuli and perform abstraction at test rather than during learning are wholly consistent with transfer phenomena.One of the most fundamental questions in cognitive psychology is whether the knowledge is stored in terms of abstract rule-like descriptions or as sets of specific instances. According to the first view, novel items or events are dealt with by applying the stored abstract rules to the novel case. According to the second view, there is some process of comparison or analogy between stored examples and the current event. The controversy between these points of view arises in the study of memory (Hintzmann,