Atheory is usually expected to explain existing experimental results and to predict new results, while an experiment is usually expected to check the validity of existing theories and to gather data for modifying them. This approach is normally presented to students as foolproof as if it were one of the basic laws of “good” science. In practice these goals are achieved in some cases, but sometimes the comparison between a theory and an experiment can be very misleading. Here I am going to discuss these unusual cases, to warn against the possible pitfalls. They may or may not be rare, but in any event it is important to bear in mind that they do exist.