In this paper we examine a series of techniques to enhance the collection and analysis of conversations on Twitter. We start from the position of seeking to understand how ordinary discussions about particular issues or controversies are unfolding on the social media platform. A key limitation of studies of topics on Twitter that rely on searching for a keyword or hashtag is that they may miss important sections of conversations around issues that do not match the keywords selected (Rambukkana, 2015, Bruns & Burgess, 2015). The Tracking Infrastructure for Social Media Analysis (TrISMA) (Bruns, Burgess & Banks et al., 2016) captures tweets of 2.8m Australian users on a continuing basis providing a comprehensive dataset that we can use to find reply chains which do not include the hashtag or keyword we are studying. Many existing methods of exploring Twitter data do not present conversation chains in a linked format (Bruns, 2012, Authors, 2010); we investigate how using network visualization might help researchers better understand the qualitative content and context of conversations.