Estimating motion from image sensors is a fundamental problem in computer vision and robotics. Event cameras are novel bio-inspired sensors that provide a signal suitable for estimating motion because their pixels naturally respond to intensity changes, which are tightly related to motions in the scene. However, event data is fundamentally different from conventional frame data, which leads us to rethink visual processing. In this talk, we focus on a single problem setting: motion estimation using an event camera, where we show an example where such a rethinking plays an important role. Furthermore, we demonstrate how the estimated motion can be further utilized to various downstream tasks, such as depth estimation, motion segmentation, intensity reconstruction, and imaging fluctuations of air density. We hope to deepen the understanding of various motion estimation tasks in the emerging field of event-based vision.