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One of the main goals of natural language processing (NLP) is to build automated systems that can understand and generate human languages. This goal has so far remained elusive. Existing hand-crafted systems can provide in-depth analysis of domain sub-languages, but are often notoriously fragile and costly to build. Existing machine-learned systems are considerably more robust, but are limited to relatively shallow NLP tasks. In this thesis, we present novel statistical methods for robust natural language understanding and generation. We focus on two important sub-tasks, semantic parsing and tactical generation. The key idea is that both tasks can be treated as the translation between natural languages and formal meaning representation languages, and therefore, can be performed using state-of-the-art statistical machine translation techniques. Specifically, we use a technique called synchronous parsing, which has been extensively used in syntax-based machine translation, as the unifying framework for semantic parsing and tactical generation. The parsing and generation algorithms learn all of their linguistic knowledge from annotated corpora, and can handle natural-language sentences that are conceptually complex.