Visual motion estimation is a computationally intensive, but important task for sighted animals. Replicating the robustness and efficiency of biological visual motion estimation in artificial systems would significantly enhance the capabilities of future robotic agents. 25 years ago, in this very journal, Carver Mead outlined his argument for replicating biological processing in silicon circuits. His vision served as the foundation for the field of neuromorphic engineering, which has experienced a rapid growth in interest over recent years as the ideas and technologies mature. Replicating biological visual sensing was one of the first tasks attempted in the neuromorphic field. In this paper we focus specifically on the task of visual motion estimation. We describe the task itself, present the progression of works from the early first attempts through to the modern day state-of-the-art, and provide an outlook for future directions in the field.