Neuro-inspired computing is a new computing paradigm that emulates the neural network for information processing. To enable the large-scale neuromorphic system, it is important to develop compact nanoscale devices to support the synaptic and neuronal functions. In this talk, I will discuss recent progress in this domain that integrates oxide based synaptic and neuronal devices in neuromorphic hardware such as machine/deep learning accelerators. First, I will discuss the desired characteristics of HfO2 based resistive synaptic devices (e.g. analog multilevel states, weight tuning linearity, variation/noises) and NbO2 based oscillation neuron devices, and show the principles of offline training and online training. Next, I will introduce the crossbar array architecture to efficiently implement the weighted sum and weight update operations that are commonly used in the machine/deep learning algorithms, and show array-level experimental demonstrations for these key operations. Lastly, I will show our recent work on doped HfO2 based ferroelectric transistor based synaptic cell design that overcomes the challenges to achieve high training accuracy for online training.