Memristive devices are two-terminal devices that can change their resistance state upon application of appropriate voltage stimuli. The resistance can be tuned over a wide resistance range enabling applications such as multibit data storage or analog computing-in-memory concepts. One of the most promising classes of memristive devices is based on the valence change mechanism in oxide-based devices. In these devices, a configurational change of oxygen defects, i.e. oxygen vacancies, leads to the change of the device resistance. A microscopic understanding of the conduction is necessary in order to design memristive devices with specific resistance properties. In this paper, we discuss the conduction mechanism proposed in the literature and propose a comprehensive, microscopic model of the conduction mechanism in this class of devices. To develop this microscopic picture of the conduction, ab initio simulation models are developed. These simulations suggest two different types of conduction, which are both limited by a tunneling through the Schottky barrier at the metal electrode contact. The difference between the two conduction mechanisms is the following: for the first type, the electrons tunnel into the conduction band and, in the second type, into the vacancy defect states. These two types of conduction differ in their current voltage relation, which has been detected experimentally. The origin of the resistive switching is identical for the two types of conduction and is based on a modification of the tunneling distance due to the oxygen vacancy induced screening of the Schottky barrier. This understanding may help to design optimized devices in terms of the dynamic resistance range for specific applications.