This paper gives an overview of the stochastic modelling approach to machine translation.Starting with the Bayes decision rule as in pattern classification and speech recognition, we show how the resulting system architecture can be structured into three parts: the language model probability, the string translation model probability and the search procedure that generates the word sequence in the target language. We discuss the properties of the system components and report results on the translation of spoken dialogues in the VERBMOBIL project. The experience obtained in the VERB-MOBIL project, in particular a largescale end-to-end evaluation, showed that the stochastic modelling approach resulted in significantly lower error rates than three competing translation approaches: the sentence error rate was 29% in comparison with 52% to 62% for the other translation approaches.