In this chapter we examine inflectional classes from a default inheritance perspective. We argue that the traditional notion of inflectional classes as monolithic entities is misleading. Instead, they should be perceived as partial entities which can be modelled in terms of a specific hierarchy for inflectional morphology. There is a point of typological contrast between languages for which a valid morphological hierarchy can be constructed, and those for which it cannot. We illustrate this point by considering inflectional classes within their wider typological space. We first look at clitic-like elements to show how they fit at one extreme of a dimension where inflectional classes are at the other end, and we provide a formal implemented account, which relies on the syntax being able to refer to the edge of a phrase in order to place the morphosyntactic features to be realized, but where the morphology does not have knowledge of the feature which expresses the information about the edge. In the absence of any distinctions which cross-cut those made in syntax there is no need for a morphological hierarchy. We then look at inflectional classes. In our case study of Russian nominals we consider the relationship between the lexemic hierarchy and the morphological hierarchy and show that the morphological hierarchy cannot be collapsed onto the lexemic hierarchy, because of the cross-cutting structure. We also show how defaults for morphology in languages such as Russian can go beyond particular parts of speech to classes such as nominals.