Data has often been stated to be “the new oil”. This is said because both oil and data can be very valuable but only after they have been pre-processed. Among other things, a challenge for creating value from data lies in realizing data exchange. This is what data marketplaces aim to do. The number of shutdowns of data marketplaces during the past years implies that their business models are not viable and that there are obstacles that should be overcome to create a data marketplace that is robust in the long run. In this research, we explore a new research context: the relationships between business models of data marketplaces and data marketplace obstacles. To do this, by the means of explorative theorizing, we first provide an overview of the obstacle categories for data marketplaces: trust, lack of governance mechanisms, privacy and control, product quality and product description, matching data providers and data buyers, data pricing mechanism, and ‘other’ that do not fall within a specific category. We then followed a multiple-case studying approach in which we subject three different real-life data marketplaces to a Business Model (BM) Stress Test on the identified obstacles. The cases were selected by theoretical sampling of the types of data marketplaces: personal data marketplaces, Internet-Of-Things (IoT) data marketplaces, and Business-to-Business (B2B) data marketplaces. By reflecting upon the results, we conclude that the assessment of the true viability of a data marketplace business model goes way beyond just the relationships between business model choices and obstacles. It is concerned with the business model strategy and dynamic capabilities of a data marketplace. We add to the literature by presenting a first explanatory model on the relationships between data marketplace business models and data marketplace obstacles. This model leads us to the practical implications of our results. These include the considerations that a data marketplace owner can take into account when making business model choices. Based on the results, we are also able to give recommendations that go beyond certain business model choices.