The concept of emergence has its roots in 19th-century philosophy. Today it is central to many computational systems which retain the hallmarks of emergence laid out much earlier. The role of emergence in creative design and its unique embodiment in shape grammars have been emphasized by March, Stiny, and others. Shape grammars generate emergent shapes -- shapes not predefined in a grammar. Emergent shapes are not only the output of a shape grammar computation; they can be the input for further computation. The history of emergence and its characterization in shape grammars are discussed here. Different sorts of shape emergence in grammars are then distinguished: anticipated, possible, and unanticipated. Unanticipated emergent shapes are shapes not premeditated by the author or user of a grammar. Generally, unanticipated shapes require on-the-spot definitions of rules to compute with them. However, for some interesting design problems, it is possible to know in advance what to do with unanticipated shapes, and to predefine rules accordingly. Special rules for computing with unanticipated shapes are proposed here. These rules allow for processes that have previously been handled extragrammatically -- outside of grammars -- to be handled within grammars. Examples of applications of these rules within a single grammar and across parallel grammars are given.