Neuromorphic cameras are emerging imaging technology that has advantages over conventional imaging sensors in several aspects including dynamic range, sensing latency, and power consumption. However, the signal-to-noise level and the spatial resolution still fall behind the state of conventional imaging sensors. In this article, we address the denoising and super-resolution problem for modern neuromorphic cameras. We employ 3D U-Net as the backbone neural architecture for such a task. The networks are trained and tested on two types of neuromorphic cameras: a dynamic vision sensor and a spike camera. Their pixels generate signals asynchronously, the former is based on perceived light changes and the latter is based on accumulated light intensity. To collect the datasets for training such networks, we design a display-camera system to record high frame-rate videos at multiple resolutions, providing supervision for denoising and super-resolution. The networks are trained in a noise-to-noise fashion, where the two ends of the network are unfiltered noisy data. The output of the networks has been tested for downstream applications including event-based visual object tracking and image reconstruction. Experimental results demonstrate the effectiveness of improving the quality of neuromorphic events and spikes, and the corresponding improvement to downstream applications with state-of-the-art performance.