Statistical machine translation (SMT) approaches extract translation knowledge automatically from parallel corpora. They additionally take advantage of monolingual text for target-side language modelling. Syntax-based SMT approaches also incorporate knowledge of source and/or target syntax by taking advantage of monolingual grammars induced from treebanks, and semantics-based SMT approaches use knowledge of source and/or target semantics in various forms. However, there has been very little research on incorporating the considerable monolingual knowledge encoded in deep, hand-built grammars into statistical machine translation. Since deep grammars can produce semantic representations, such an approach could be used for realization as well as MT. In this thesis I present a hybrid approach combining some of the knowledge in a deep hand-built grammar, the English Resource Grammar (ERG), with a statistical machine translation approach. The ERG is used to parse the source sentences to obtain Dependency Minimal Recursion Semantics (DMRS) representations. DMRS representations are subsequently transformed to a form more appropriate for SMT, giving a parallel corpus with transformed DMRS on the source side and aligned strings on the target side. The SMT approach is based on hierarchical phrase-based translation (Hiero). I adapt the Hiero synchronous context-free grammar (SCFG) to comprise graph-to-string rules. DMRS graph-to-string SCFG is extracted from the parallel corpus and used in decoding to transform an input DMRS graph into a target string either for machine translation or for realization. I demonstrate the potential of the approach for large-scale machine translation by evaluating it on the WMT15 English-German translation task. Although the approach does not improve on a state-of-the-art Hiero implementation, a manual investigation reveals some strengths and future directions for improvement. In addition to machine translation, I apply the approach to the MRS realization task. The approach produces realizations of high quality, but its main strength lies in its robustness. Unlike the established MRS realization approach using the ERG, the approach proposed in this thesis is able to realize representations that do not correspond perfectly to ERG semantic output, which will naturally occur in practical realization tasks. I demonstrate this in three contexts, by realizing representations derived from sentence compression, from robust parsing, and from the transfer-phase of an existing MT system. In summary, the main contributions of this thesis are a novel architecture combining a statistical machine translation approach with a deep hand-built grammar and a demonstration of its practical usefulness as a large-scale machine translation system and a robust realization alternative to the established MRS realization approach.