Accurately predicting the future fluid is important to extensive areas such as meteorology, oceanology, and aerodynamics. However, since the fluid is usually observed from an Eulerian perspective, its moving and intricate dynamics are seriously obscured and confounded in static grids, bringing thorny challenges to the prediction. This paper introduces a new Lagrangian-Eulerian combined paradigm to tackle the tanglesome fluid dynamics. Instead of solely predicting the future based on Eulerian observations, we propose DeepLag to discover hidden Lagrangian dynamics within the fluid, by tracking movements of adaptively sampled key particles. DeepLag utilizes the proposed multiscale Eulag Block to communicate the learned Eulerian and Lagrangian features by two transformer blocks, where the Lagrangian movement of the tracked particles is inferred from Eulerian observations, and their accumulated Lagrangian dynamics information is incorporated into global Eulerian evolving features to guide future prediction respectively. Tracking key particles not only provides a clear and interpretable clue for fluid dynamics but also makes our model free from modeling complex correlations among massive grids for better efficiency. Experimentally, DeepLag excels in three challenging fluid prediction tasks, covering both 2D and 3D, simulated and real-world fluids.