We investigate a new approach for SMT system training within the streaming model of computation. We develop and test incrementally retrainable models which, given an incoming stream of new data, can efficiently incorporate the stream data online. A naive approach using a stream would use an unbounded amount of space. Instead, our online SMT system can incorporate information from unbounded incoming streams and maintain constant space and time. Crucially, we are able to match (or even exceed) translation performance of comparable systems which are batch retrained and use unbounded space. Our approach is particularly suited for situations when there is arbitrarily large amounts of new training material and we wish to incorporate it efficiently and in small space. The novel contributions of this thesis are: 1. An online, randomised language model that can model unbounded input streams in constant space and time. 2. An incrementally retrainable translationmodel for both phrase-based and grammarbased systems. The model presented is efficient enough to incorporate novel parallel text at the single sentence level. 3. Strategies for updating our stream-based language model and translation model which demonstrate how such components can be successfully used in a streaming translation setting. This operates both within a single streaming environment and also in the novel situation of having to translate multiple streams. 4. Demonstration that recent data from the stream is beneficial to translation performance. Our stream-based SMT system is efficient for tackling massive volumes of new training data and offers-up new ways of thinking about translating web data and dealing with other natural language streams.