In state-of-the-art phrase-based statistical machine translation systems (SMT), modelling phrase reorderings is an important need to enhance naturalness of the translate outputs, particularly when the grammatical structures of the language pairs differ significantly. The challenge in developing machine learning methods for machine translation can be summarised in two points. First is the ability to characterise language features such as morphology, syntax and semantics. Second is adapting complex learning algorithms to process large corpora. Posing phrase movements as a classification problem, we exploit recent developments in solving large-scale SVM, Multiclass SVM and Multinomial Logistic Regression. Using dual coordinate descent methods for learning, we provide a mechanism to shrink the amount of training data required for each iteration. Hence, we produce significant saving in time and memory while preserving the accuracy of the models. These efficient classifiers allow us to build large-scale discriminative reordering models. We also explore a generative learning approach namely naive Bayes. Our Bayesian model is shown to be superior to the widely-used lexicalised reordering model. It is fast to train and the storage requirement is many times smaller than the lexicalised model. Although discriminative models might achieve higher accuracy than naive Bayes, the absence of iterative learning is a critical advantage for very large corpora. Our reordering models are fully integrated with the Moses machine translation system, widely used in the community. Evaluated in large-scale translation tasks, our model have proved successful for two very different language pairs: Arabic-English and German-English.