AbstractNegation and modality are two important grammatical phenomena that have attracted recent research attention as they can contribute to extra-propositional meaning aspects, among with factuality, attribution, irony and sarcasm. These aspects go beyond analysis such as semantic role labeling, and modeling them is important as a step towards a higher level of language understanding, which is needed for practical applications such as sentiment analysis. In this talk, I will go beyond English, and I will discuss how negation and modality are expressed in other languages. I will also go beyond sentiment analysis and I will present some challenges that the two phenomena pose for machine translation (MT). In particular, I will demonstrate how contemporary MT systems fail on them, and I will discuss some possible solutions.