In this work, we will focus on the role that new nonvolatile resistive memory technologies can play in emerging fields of application, such as non-volatile logic circuits or neuromorphic circuits, to save energy and increase performance. Concerning the introduction of non-volatile functionalities at the logic level, we will demonstrate hybrid CMOS logic plus ReRAM (specifically CBRAM and OXRAM) circuits for ultra low power FPGA and fixed-logic IC design, as Non Volatile Flip-Flops. Concerning neuromorphic circuits, we will focus on the emulation of synaptic plasticity effects with resistive memory synapses. We will present large-scale energy efficient neuromorphic systems based on ReRAM as stochastic-binary synapses. Prototype applications such as complex visual- and auditory-pattern extraction will be also discussed using feedforward spiking neural networks.