In this talk I will describe the traditional approaches to morphological derivation in order to provide context for a discussion of computational approaches to the same. Linguistic models of morphological derivation have a tendency to assume a well defined correspondence between inflected forms and constituents in the lexicon, an assumption which exhibits some deficiences when considering more complex morphological processes, such as the combined effects of morphological and phonological processes on derivational models. Modelling and evaluating possible morpho-phonological derivations has been considered computationally intensive with a non-linear increases in computational complexity proportional to the increasing size of a lexicon. A number of proposals have been made at a conceptual level for morphological parsing in a massively parallel mode in order to derive relations between the lexicon and inflected forms. In this talk we will consider a number of benefits and constraints of parallel computational models for morpho-phonological derviation from the lexicon.