Sarcasm is a linguistic expression often used to communicate the opposite of what is said, usually something that is very unpleasant with an intention to insult or ridicule. Inherent ambiguity in sarcastic expressions makes sarcasm detection very difficult. In this work, we focus on detecting sarcasm in textual conversations, written in English, from various social networking platforms and online media. To this end, we develop an interpretable deep learning model using multi-head self-attention and gated recurrent units. We show the effectiveness and interpretability of our approach by achieving state-of-the-art results on datasets from social networking platforms, online discussion forums, and political dialogues.