Graphical models are a powerful statistical abstraction that are capable of representing important mathematical properties of probability distributions in a visual and intuitive way. Recently, they have started being investigated for use in understanding and processing natural language. In the first half of this talk, we will give a broad overview of graphical modeling methodologies, and how they can be used for natural language processing. In the second half, we will cover our efforts in applying graphical models to the statistical machine translation problem. In particular, we will demonstrate how various forms of graphical model can be used to express some standard machine translation systems, and will describe how we have begun using them for various translation tasks. We will emphasize the representational and computational aspects of our efforts.