Smartphones contain sensors that provide information about the user of the device. Studying smartphones, therefore, provides an invaluable window into the behavioral patterns of users. In this work, we describe an open infrastructure that provides research communities with principled access to mobile devices and their sensors. Our platform, the Sensibility Testbed, is a free, community-driven platform for mobile devices. It provides secure data access to user-owned mobile devices while preserving user privacy. The unified programmable interface to sensors on heterogeneous devices in the Sensibility Testbed enables research scientists to design and deploy experiments that run across large numbers of devices, for example to measure the coverage and performance of cellular and WiFi networks. The Sensibility Testbed makes the sensing capabilities of smartphones more accessible to a broad range of researchers.