Many urgent problems that societies currently face—from climate change to a global pandemic—require citizens to engage with scientific information as members of democratic societies as well as to solve problems in their personal lives. Most often, to solve their epistemic aims (aims directed at achieving knowledge and understanding) regarding such socio-scientific issues, individuals search for information online, where there exists a multitude of possibly relevant and highly interconnected sources of different perspectives, sometimes providing conflicting information. The paper provides a review of the literature aimed at identifying (a) constraints and affordances that scientific knowledge and the online information environment entail and (b) individuals' cognitive and motivational processes that have been found to hinder, or conversely, support practices of engagement (such as critical information evaluation or two-sided dialogue). Doing this, a conceptual framework for understanding and fostering what we call online engagement with scientific information is introduced, which is conceived as consisting of individual engagement (engaging on one's own in the search, selection, evaluation, and integration of information) and dialogic engagement (engaging in discourse with others to interpret, articulate and critically examine scientific information). In turn, this paper identifies individual and contextual conditions for individuals' goal-directed and effortful online engagement with scientific information.