The thesis investigates the formal semantics of temporal indexical expressions in English. Examples of such expressions include now, tomorrow and last year. In the past, research has concentrated on instances of such expressions which have two major properties. These indexicals are sensitive to extralinguistic context, and while they do possess descriptive meaning, that meaning does not appear within the propositions which correspond to utterances of the sentences which contain the indexicals. The thesis argues that this line of research has neglected a significant body of natural language evidence in which indexicals display rather different behaviour. We term indexicals from the first group unbound, and indexicals from the second group bound. Given these two domains of indexical evidence, the thesis sets out to achieve three primary aims. The first aim is to provide a formal semantic representation of both bound and unbound indexicals which systematically relates them, while distinguishing them from non-indexical expressions. To establish this aim, we informally investigate the relationship between the two types of indexical, and propose a unifying generalisation. This generalisation is then embedded within an existing but novel semantic system, due to Richards, called IQ. IQ is an interval-based semantics for tenses and temporal quantifiers in English which makes use of double-indexing. IQ must be modified so as to properly accommodate indexicals. With a new representation in hand, we demonstrate that the thesis can adequately treat both types of indexical occurrence. The second aim of the thesis is to assess the effects of the incorporation of the two types of indexical on the semantic entities of IQ. The propositions of IQ already include two major types: value free and value specific. Using the new representation of indexicals, the thesis shows that there are further varieties of the value free proposition. These propositions are then compared with Kaplan's contents, Frege's thoughts and Russell's propositions. The final aim is to establish a rigorous formulation of a fragment of the version of IQ derived in the thesis. Given this formulation, it is possible to assess its position relative to a landmark in the logic of indexicals. Using mathematical techniques, the thesis proves that the tense operators and indexical operators of the final version of IQ have particular properties which distinguish them from those in other indexical logics also based on double-indexing.