The technology-driven transformation process continues to spawn novel, growth-oriented digital application domains and platforms. The user base of these society-level software systems consists of a larger proportion of the community and that involve a large set of stakeholder groups. In case of an incident there is a public demand from a variety of stakeholders for multilateral intervention in order to correct the behavior of the software system. For software engineering as a technical discipline that has been fostered and matured in corporate and organizational context, this is a major challenge because it has to deal with a multitude of multidisciplinary stakeholders and their concerns. In order to stimulate further discussions, we discuss software governance on societal level and identify future research challenges of this increasingly relevant topic. © 2020 ACM.