In my talk, I will review several such applications based on metal-oxide memristors which were a recent focus of my group. I will start with stateful material implication logic, which was originally suggested by HPL group. In our work, we showed that 3D version of this logic allows resolving Feynman grand challenge of implementing 8-bit adder in a volume smaller than 50-nm cube. I will then review our experimental work on memristor-based security primitives, in which we utilized device variations and their nonlinear I-Vs to demonstrate functionality and physical performance superior to those of conventional approaches. Finally, I will discuss Race Logic, a novel computing paradigm in which information is encoded in timing of the signals, so that a particular problem is mapped to a circuit with controllable memristor-based delay elements, and the solution is provided by measuring the time for the injected signals to propagate via circuit. Due to direct encoding of the computation to the underlying physics, Race Logic is extremely energy efficient for a variety of problems, such as bioinformatics and neurocomputing. I will conclude my talk with a summary on the device/material challenges, and potential future work, specific to the discussed applications.