Memristive devices have attracted tremendous interests because of their highly desirable properties such as a simple structure, low switching voltage, fast switching speed, excellent scalability, multiple conductance states and great compatibility with the Complementary Metal–Oxide–Semiconductor technology. Hence, they stand out as promising candidates for next-generation non-volatile memory and electronic synapses in artificial neural network. This thesis reports systematic studies of the memristive switching phenomena in oxide based material systems, in aspects of materials engineering, switching mechanism and novel applications. We demonstrated efficient ways of engineering device performances such as metal doping and further presented a highly reliable hafnium oxide based memristor with tantalum conduction channel(s). Finally, we built an electronic emulator of conditioning and extinction with two series connected ionic and electronic memristors and implemented a novel true random number generator based on stochastic diffusive memristors, paving the way for the adoption of memristors for artificial intelligence and hardware security.