The modal interpretation of quantum mechanics is a no-collapse interpretation that provides a rule for assigning properties to quantum mechanical systems, depending on their (reduced) quantum state, whether this state be pure or mixed. The modal interpretation was originally developed by Kochen (1985), Dieks (1989) and Healey (1989) (with slight differences) modifying ideas by Van Fraassen (1973, 1991), and was further developed by Vermaas and Dieks (1995) and Clifton (1995). In the original version, the rule for assigning properties is applied to all quantum systems. However, a recent series of no-go theorems by Bacciagaluppi (1995), Clifton (1996) and Vermaas (1997) has shown that this unrestricted application of the rule leads to contradictions. This has prompted some authors (Bacciagaluppi and Dickson, 1999; Dieks, 1998) to restrict application of the rule only to "elementary" or "atomic" systems. We call this version the atomic modal interpretation. In this paper, we shall describe the no-go results, and discuss the picture yielded by the atomic modal interpretation. We shall proceed as follows.