This paper seeks to document the current state of the art in 'uplift modelling'—the practice of modelling the change in behaviour that results directly from a specified treatment such as a marketing intervention. We include details of the Significance-Based Uplift Trees that have formed the core of the only packaged uplift modelling software currently available. The paper includes a summary of some of the results that have been delivered using uplift modelling in practice, with examples drawn from demand-stimulation and customer-retention applications. It also surveys and discusses approaches to each of the major stages involved in uplift modelling—variable selection, model construction, quality measures and post-campaign evaluation—all of which require different approaches from traditional response modelling.