Modern science is relying on software more than ever. The behavior and outcomes of this software shape the scientific and public discourse on important topics like climate change, economic growth, or the spread of infections. Most researchers creating software for scientific purposes are not trained in Software Engineering. As a consequence, research software is often developed ad hoc without following stringent processes. With this paper, we want to characterize research software as a new application domain that needs attention from the Requirements Engineering community. We conducted an exploratory study based on 8 interviews with 12 researchers who develop software. We describe how researchers elicit, document, and analyze requirements for research software and what processes they follow. From this, we derive specific challenges and describe a vision of Requirements Engineering for research software.