In this article, we argue that students' unfolding discourse on socio-scientific issues (SSI) can be fruitfully analyzed by using dialogical theories of language and communication (Bakhtin 1986; Linell 2009). While research in science education often reports on how individual reasoning changes when bringing SSI into the classroom, we argue for the relevance of analyzing "how the individual is 'in dialogue' with present as well as remote interlocutors and contexts on the internet." We suggest that the analytical approach is particularly sensitized to illuminate how students' handle multiple perspectives. A dialogical perspective takes as its premise that SSI are part of society, where politicians, interest groups, and scientists engage in debates and offer perspectives that are often in conflict. Rather than assuming that "the individual student" is the primary unit for analysis, a dialogical approach is premised on an analysis that incorporates several perspectives and voices--a multivocality that also resides with the individual. Arguing for the relevance of this analytical approach to studies of SSI in the classroom, we analyze a group of students in upper secondary school as they discuss hydraulic fracturing after having worked with online data. The results illuminate how students discursively manage multivocality and multimodality inherent in the following SSI online. We describe a set of discursive means that the students use to handle the many perspectives involved when communicating about the issue. In addition, we describe and articulate what kind of communicative competences that are involved and, hence, could be cultivated through education, when engaging in public debates.