Word alignment is a fundamental and crucial component in Statistical Machine Translation (SMT) systems. Despite the enormous progress made in the past two decades, this task remains an active research topic simply because the quality of word alignment is still far from optimal. Most state-of-the-art word alignment models are grounded on statistical learning theory treating word alignment as a general sequence alignment problem, where many linguistically motivated insights are not incorporated. In this thesis, we propose new word alignment models with linguistically motivated constraints in a bid to improve the quality of word alignment for Phrase-Based SMT systems (PB-SMT). We start the exploration with an investigation into segmentation constraints for word alignment by proposing a novel algorithm, namely word packing, which is motivated by the fact that one concept expressed by one word in one language can frequently surface as a compound or collocation in another language. Our algorithm takes advantage of the interaction between segmentation and alignment, starting with some segmentation for both the source and target language and updating the segmentation with respect to the word alignment results using state-of-the-art word alignment models; thereafter a refined word alignment can be obtained based on the updated segmentation. In this process, the updated segmentation acts as a hard constraint on the word alignment models and reduces the complexity of the alignment models by generating more 1-to-1 correspondences through word packing. Experimental results show that this algorithm can lead to statistically significant improvements over the state-of-the-art word alignment models. Given that word packing imposes "hard" segmentation constraints on the word aligner, which is prone to introducing noise, we propose two new word alignment models using syntactic dependencies as soft constraints. The first model is a syntactically enhanced discriminative word alignment model, where we use a set of feature functions to express the syntactic dependency information encoded in both source and target languages. One the one hand, this model enjoys great flexibility in its capacity to incorporate multiple features; on the other hand, this model is designed to facilitate model tuning for different objective functions. Experimental results show that using syntactic constraints can improve the performance of the discriminative word alignment model, which also leads to better PB-SMT performance compared to using state-of-the-art word alignment models. The second model is a syntactically constrained generative word alignment model, where we add in a syntactic coherence model over the target phrases in the context of HMM word-to-phrase alignment. The advantages of our model are that (i) the addition of the syntactic coherence model preserves the efficient parameter estimation procedures; and (ii) the flexibility of the model can be increased so that it can be tuned according to different objective functions. Experimental results show that tuning this model properly leads to a significant gain in MT performance over the state-of-the-art.