In the past few decades, technological progress has led to the digitization and digitalization of economies into what one could now call digital economies. The COVID-19 pandemic will accelerate the development of the digital economy. In a digital economy, digital entrepreneurs pursue opportunities to produce and trade in digital artifacts on digital artifact stores or platforms, and/or to create these digital artifact stores or platforms themselves. There is a well-recognized need for more research on digital entrepreneurship. As such, this paper provides an overview of the central research questions currently being pursued in this field. These include questions such as: What is digital entrepreneurship? What is different in the digital economy from an entrepreneurial perspective? What is the impact of digitalization - and big data - on business models and entrepreneurship? How can digital entrepreneurship be supported and regulated? The paper identifies areas of neglect, and makes proposals for future research.