In this dissertation, I start with an analysis of negation in eleven benchmark corpora covering six Natural Language Understanding (NLU) tasks. With a thorough investigation, I first show that (a) these benchmarks contain fewer negations compared to general-purpose English and (b) the few negations they contain are often unimportant. Further, my empirical studies demonstrate that state-of-the-art transformers trained using these corpora obtain substantially worse results with the instances that contain negation, especially if the negations are important. Second, I investigate whether translating negation is also an issue for modern machine translation (MT) systems. My studies find that indeed the presence of negation can significantly impact translation quality, in some cases resulting in reductions of over 60%. In light of these findings, I investigate strategies to better understand the semantics of negation. I start with identifying the focus of negation. I develop a neural model that takes into account the scope of negation, context from neighboring sentences, or both. My best proposed system obtains an accuracy improvement of 7.4% over prior work. Further, I analyze the main error categories of the systems through a detailed error analysis. Next, I explore more practical ways to understand the semantics of negation. I consider …