There have been important developments in computationally oriented linguistic theory in the last 10 years, in particular, the development of formalisms based on UNIFICATION. This is already important as regards Machine Translation research, and will become increasingly so as the next generation of practical MT systems evolves. One purpose of this paper is tutorial — to give an overview of these developments, to say why they are positive and to explore their application in the context of MT. The paper also has a non-tutorial aim of conceptual clarification: we think these developments contain a number of options that are interestingly different.