In the context of Open Science, the importance of Borgman’s conundrum challenges that have been initially formulated concerning the difficulties to share Research Data is well known: which Research Data might be shared, by whom, with whom, under what conditions, why, and to what effects. We have recently reviewed the concepts of Research Software and Research Data, concluding with new formulations for their definitions, and proposing answers to these conundrum challenges for Research Data. In the present work we extend the consideration of the Borgman’s conundrum challenges to Research Software, providing answers to these questions in this new context. Moreover, we complete the initial list of questions/answers, by asking how and where the Research Software may be shared. Our approach begins by recalling the main issues involved in the Research Software definition, and its production context in the research environment, from the Open Science perspective. Then we address the conundrum challenges for Research Software by exploring the potential similarities and differences regarding our answers for these questions in the case of Research Data. We conclude emphasizing the usefulness of the followed methodology, exploiting the parallelism between Research Software and Research Data in the Open Science environment.