Recently, computational argumentation has attracted a lot of attention in the NLP community. In this talk, I will first give a short overview of this new field, reviewing the recent advances in different sub-fields. Then I'll briefly present IBM Debater Project. After that, I will talk about two research problems I've been working together with my colleagues over the last two years: evidence detection and argument relation classification. Finally, I'll outline a few challenging research questions and talk about some of my ongoing work in this area.