Electrical switching, manifesting itself in the nonlinear current-voltage characteristics with S- and N-type NDR (negative differential resistance), is inherent in a variety of materials, in particular, transition metal oxides. Although this phenomenon has been known for a long time, recent suggestions to use oxide-based switching elements as neuristor synapses and relaxation-oscillation circuit components have resumed the interest in this area. In the present review, we describe the experimental facts and theoretical models, mainly on the basis of the Mott transition in vanadium dioxide as a model object, of the switching effect with special emphasis on the emerging applied potentialities for oxide electronics.