This paper analyses whether competition law can help to solve problems of access to data and interoperability in IoT ecosystems, where often one firm has exclusive control of the data produced by a smart device (and of the technical access to this device). Such a gatekeeper position can lead to the elimination of competition for aftermarket and other complementary services in such IoT ecosystems. This problem is analysed both from an economic and a legal perspective, and also generally for IoT ecosystems as well as for the much discussed problems of "access to in-vehicle data and resources" in connected cars, where the "extended vehicle" concept of the car manufacturers leads to such positions of exclusive control. The paper analyses, in particular, the competition rules about abusive behavior of dominant firms (Art. 102 TFEU) and of firms with "relative market power" (§ 20 (1) GWB) in German competition law. These provisions might offer (if appropriately applied and amended) at least some solutions for these data access problems. Competition law, however, might not be sufficient for dealing with all or most of these problems, i.e. that also additional solutions might be needed (data portability, direct data (access) rights, or sector-specific regulation).