The thesis assumes that a theory of language should be evaluated with reference to both linguistic and psycholinguistic evidence, and that the processor makes use of the rules of the grammar directly. It contends that most current linguistic theories are not adequate in this respect, and concentrates on one major issue, that these theories are unable to represent the fact that we can begin an interpretation of an utterance before it is completed. It is argued that this is due to the assumption that sentences should be represented by the devices of phrase structure grammar which includes rigid, non-overlapping constituents. It suggests that these should be replaced by a flexible notion of constituency, based on a generalized notion of dependency, which is called dependency constituency. The thesis then shows how this notion can be represented in the grammatical framework known as the Lambek Calculus, by means of a very simple restriction on the permitted opeations. It then shows how this allows a new characterization of strings that can be coordinated, which it is argued captures the relevant data better than competing theories. The thesis then proposes an account of human sentence processing based on dependency constituency. It the applies the account of dependency constituency to unbounded dependencies, and suggests that the treatment is more parsimonious than alternatives based on phrase structure grammar that make use of otherwise unmotivated mechanisms such as empty categories. It shows how experimental evidence that is usually interpreted in terms of theories using empty categories can be reinterpreted in terms that do not use these devices. But the next chapter goes further, and shows how it is possible to distinguish between a processing theory with empty categories and a theory without empty categories. It is claimed that the evidence supports a theory without these devices, and so a grammatical theory that bears any relation to sentence processing should avoid their postulation.