This talk will introduce effective methods for learning unknown time-dependent differential equations from measurement data. We will explore the importance of using many short bursts of trajectory data instead of a few long trajectories. We will present several data-driven modeling strategies using deep neural networks. It will be shown that residual networks are particularly suitable for equation discovery, as they can produce an exact time integrator for numerical predictions. Additionally, the deep learning of unknown partial differential equations in modal or nodal spaces will be discussed, along with recent advances in structure-preserving learning approaches for unknown equations.