This thesis explores the application of data-driven machine translation (MT) to sign languages (SLs). The provision of an SL MT system can facilitate communication between Deaf and hearing people by translating information into the native and preferred language of the individual. We begin with an introduction to SLs, focussing on Irish Sign Language - the native language of the Deaf in Ireland. We describe their linguistics and mechanics including similarities and differences with spoken languages. Given the lack of a formalised written form of these languages, an outline of annotation formats is discussed as well as the issue of data collection. We summarise previous approaches to SL MT, highlighting the pros and cons of each approach. Initial experiments in the novel area of example-based MT for SLs are discussed and an overview of the problems that arise when automatically translating these manual-visual languages is given. Following this we detail our data-driven approach, examining the MT system used and modifications made for the treatment of SLs and their annotation. Through sets of automatically evaluated experiments in both language directions, we consider the merits of data-driven MT for SLs and outline the mainstream evaluation metrics used. To complete the translation into SLs, we discuss the addition and manual evaluation of a signing avatar for real SL output.