Our daily online conversations with friends, family, colleagues, and strangers weave an intricate network of interactions. From these networked discussions emerge themes and topics that transcend the scope of any individual conversation. In turn, these themes direct the discourse of the network and continue to ebb and flow as the interactions between individuals shape the topics themselves. This rich loop between interpersonal conversations and overarching topics is a wonderful example of a complex system: the themes of a discussion are more than just the sum of its parts. Some of the most socially relevant topics emerging from these online conversations are those pertaining to racial justice issues. Since the shooting of Black teenager Michael Brown by White police officer Darren Wilson in Ferguson, Missouri, the protest hashtag #BlackLivesMatter has amplified critiques of extrajudicial shootings of Black Americans. In response to #BlackLivesMatter, other online users have adopted #AllLivesMatter, a counter-protest hashtag whose content argues that equal attention should be given to all lives regardless of race. Together these contentious hashtags each shape clashing narratives that echo previous civil rights battles and illustrate ongoing racial tension between police officers and Black Americans. These narratives have taken place on a massive scale with millions of online posts and articles debating the sentiments of ``black lives matter'' and ``all lives matter.'' Since no one person could possibly read everything written in this debate, comprehensively understanding these conversations and their underlying networks requires us to leverage tools from data science, machine learning, and natural language processing. In Chapter 2, we utilize methodology from network science to measure to what extent #BlackLivesMatter and #AllLivesMatter are ``slacktivist'' movements, and the effect this has on the diversity of topics discussed within these hashtags. In Chapter 3, we precisely quantify the ways in which the discourse of #BlackLivesMatter and #AllLivesMatter diverge through the application of information-theoretic techniques, validating our results at the topic level from Chapter 2. These entropy-based approaches provide the foundation for powerful automated analysis of textual data, and we explore more generally how they can be used to construct a human-in-the-loop topic model in Chapter 4. Our work demonstrates that there is rich potential for weaving together social science domain knowledge with computational tools in the study of language, networks, and social movements.