This paper presents an overview of Statistical Machine Translation (SMT), which is currently the dominant approach in Machine Translation (MT) research. In Way and Hearne (2011), we describe how central linguists and translators are to the MT process, so that SMT developers and researchers may better understand how to include these groups in continuing to advance the state-of-the-art. If these constituencies are to make an impact in the field of MT, they need to know how their input is used by SMT systems. Accordingly, our objective in this paper is to present the basic principles underpinning SMT in a way that linguists and translators will find accessible and useful.