Memristive devices are extensively investigated as non-volatile memory elements due to their variable resistance that is adjustable by electrical stimuli. They are promising for, e.g., neuromorphic circuits, which aim to replicate biological data processing to extend the computing capabilities of today's digital information technology, especially for data-intensive tasks. This dissertation focuses on analog interface-type devices and digital filamentary-type devices based on binary metal oxides. The analog devices are fabricated on 100 mm wafers, the current-voltage (I-V) characteristics are statistically evaluated, and the engineering of different read-out and switching parameters by up to several orders of magnitude is presented. The plasma conditions of the sputter deposition process are probed, and material properties are investigated by transmission electron microscopy (TEM), electron energy loss spectroscopy (EELS), as well as synchrotron-based X-ray photoelectron spectroscopy (XPS) and depth-dependent hard X-ray photoelectron spectroscopy (HAXPES) on functional devices. A device model is deduced that considers electron trapping/de-trapping within HfO2 as the switching mechanism that modulates a Schottky barrier. The spectroscopic evidence for the electronic switching mechanism in interface-type memristive devices should be emphasized. The utilized digital resistive random access memory (RRAM) devices were developed at the IHP in Frankfurt/Oder (Germany). The inherent randomness of the switching process is exploited to emulate stochastic synaptic plasticity in neuromorphic networks to learn images with novel supervised and unsupervised algorithms, partly realized with hardware synapses. It is further shown that the devices can potentially be used for computing matrix-vector-multiplications (MVMs) directly in-memory when storing pre-trained synaptic weights of an artificial neural network (ANN)