Augmenting Statistical Machine Translation (SMT) systems with syntactic information aims at improving translation quality. Hierarchical Phrase-Based (HPB) SMT takes a step toward incorporating syntax in Phrase-Based (PB) SMT by modelling one aspect of language syntax, namely the hierarchical structure of phrases. Syntax Augmented Machine Translation (SAMT) further incorporates syntactic information extracted using context free phrase structure grammar (CF-PSG) in the HPB SMT model. One of the main challenges facing CF-PSG-based augmentation approaches for SMT systems emerges from the difference in the definition of the constituent in CF-PSG and the ‘phrase’ in SMT systems, which hinders the ability of CF-PSG to express the syntactic function of many SMT phrases. Although the SAMT approach to solving this problem using ‘CCG-like’ operators to combine constituent labels improves syntactic constraint coverage, it significantly increases their sparsity, which restricts translation and negatively affects its quality. In this thesis, we address the problems of sparsity and limited coverage of syntactic constraints facing the CF-PSG-based syntax augmentation approaches for HPB SMT using Combinatory Cateogiral Grammar (CCG). We demonstrate that CCG’s flexible structures and rich syntactic descriptors help to extract richer, more expressive and less sparse syntactic constraints with better coverage than CF-PSG, which enables our CCG-augmented HPB system to outperform the SAMT system. We also try to soften the syntactic constraints imposed by CCG category nonterminal labels by extracting less fine-grained CCG-based labels. We demonstrate that CCG label simplification helps to significantly improve the performance of our CCG category HPB system. Finally, we identify the factors which limit the coverage of the syntactic constraints in our CCG-augmented HPB model. We then try to tackle these factors by extending the definition of the nonterminal label to be composed of a sequence of CCG categories and augmenting the glue grammar with CCG combinatory rules. We demonstrate that our extension approaches help to significantly increase the scope of the syntactic constraints applied in our CCG-augmented HPB model and achieve significant improvements over the HPB SMT baseline.