Tactile sensing is crucial for robots aiming to achieve human-level dexterity. Among tactile-dependent skills, tactile-based object tracking serves as the cornerstone for many tasks, including manipulation, in-hand manipulation, and 3D reconstruction. In this work, we introduce NormalFlow, a fast, robust, and real-time tactile-based 6DoF tracking algorithm. Leveraging the precise surface normal estimation of vision-based tactile sensors, NormalFlow determines object movements by minimizing discrepancies between the tactile-derived surface normals. Our results show that NormalFlow consistently outperforms competitive baselines and can track low-texture objects like table surfaces. For long-horizon tracking, we demonstrate when rolling the sensor around a bead for 360 degrees, NormalFlow maintains a rotational tracking error of 2.5 degrees. Additionally, we present state-of-the-art tactile-based 3D reconstruction results, showcasing the high accuracy of NormalFlow. We believe NormalFlow unlocks new possibilities for high-precision perception and manipulation tasks that involve interacting with objects using hands. The video demo, code, and dataset are available on our website: https://joehjhuang.github.io/normalflow.